About: Lozanić's triangle

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Lozanić's triangle (sometimes called Losanitsch's triangle) is a triangular array of binomial coefficients in a manner very similar to that of Pascal's triangle. It is named after the Serbian chemist Sima Lozanić, who researched it in his investigation into the symmetries exhibited by rows of paraffins (archaic term for alkanes). The first few lines of Lozanić's triangle are listed in (sequence in the OEIS). The diagonals next to the edge diagonals contain the positive integers in order, but with each integer stated twice OEIS: .

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rdfs:label	Lozanić's triangle (en)
rdfs:comment	Lozanić's triangle (sometimes called Losanitsch's triangle) is a triangular array of binomial coefficients in a manner very similar to that of Pascal's triangle. It is named after the Serbian chemist Sima Lozanić, who researched it in his investigation into the symmetries exhibited by rows of paraffins (archaic term for alkanes). The first few lines of Lozanić's triangle are listed in (sequence in the OEIS). The diagonals next to the edge diagonals contain the positive integers in order, but with each integer stated twice OEIS: . (en)
dct:subject	Triangles of numbers Factorial and binomial topics
Wikipage page ID	4187401 (xsd:integer)
Wikipage revision ID	1086228766 (xsd:integer)
Link from a Wikipage to another Wikipage	Triangles of numbers Binomial coefficient Interleave sequence Factorial and binomial topics Sima Lozanić Alkane Fibonacci number Pascal's triangle Square number Triangular array Pronic number dbr:Alkane_number
Link from a Wikipage to an external page	http://oeis.org/classic.html
sameAs	Lozanić's triangle Lozanić's triangle Lozanić's triangle
dbp:wikiPageUsesTemplate	dbt:OEIS dbt:Short_description dbt:OEIS2C
has abstract	Lozanić's triangle (sometimes called Losanitsch's triangle) is a triangular array of binomial coefficients in a manner very similar to that of Pascal's triangle. It is named after the Serbian chemist Sima Lozanić, who researched it in his investigation into the symmetries exhibited by rows of paraffins (archaic term for alkanes). The first few lines of Lozanić's triangle are 1 1 1 1 1 1 1 2 2 1 1 2 4 2 1 1 3 6 6 3 1 1 3 9 10 9 3 1 1 4 12 19 19 12 4 1 1 4 16 28 38 28 16 4 1 1 5 20 44 66 66 44 20 5 1 1 5 25 60 110 126 110 60 25 5 1 1 6 30 85 170 236 236 170 85 30 6 1 1 6 36 110 255 396 472 396 255 110 36 6 1 1 7 42 146 365 651 868 868 651 365 146 42 7 1 1 7 49 182 511 1001 1519 1716 1519 1001 511 182 49 7 11 8 56 231 693 1512 2520 3235 3235 2520 1512 693 231 56 8 1 listed in (sequence in the OEIS). Like Pascal's triangle, outer edge diagonals of Lozanić's triangle are all 1s, and most of the enclosed numbers are the sum of the two numbers above. But for numbers at odd positions k in even-numbered rows n (starting the numbering for both with 0), after adding the two numbers above, subtract the number at position (k − 1)/2 in row n/2 − 1 of Pascal's triangle. The diagonals next to the edge diagonals contain the positive integers in order, but with each integer stated twice OEIS: . Moving inwards, the next pair of diagonals contain the "quarter-squares" (OEIS: ), or the square numbers and pronic numbers interleaved. The next pair of diagonals contain the l(6, n) (OEIS: ). And the next pair of diagonals contain the alkane numbers l(7, n) (OEIS: ), while the next pair has the alkane numbers l(8, n) (OEIS: ), then alkane numbers l(9, n) (OEIS: ), then l(10, n) (OEIS: ), l(11, n) (OEIS: ), l(12, n) (OEIS: ), etc. The sum of the nth row of Lozanić's triangle is (OEIS: lists the first thirty values or so). The sums of the diagonals of Lozanić's triangle intermix with (where Fx is the xth Fibonacci number). As expected, laying Pascal's triangle over Lozanić's triangle and subtracting yields a triangle with the outer diagonals consisting of zeroes (OEIS: , or OEIS: for a version without the zeroes). This particular difference triangle has applications in the chemical study of catacondensed polygonal systems. (en)
prov:wasDerivedFrom	wikipedia-en:Lozanić's_triangle?oldid=1086228766&ns=0
page length (characters) of wiki page	3858 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Lozanić's_triangle
is Link from a Wikipage to another Wikipage of	136 (number) Sima Lozanić 72 (number) Pascal's triangle List of factorial and binomial topics Triangular array List of triangle topics Lozanic's triangle Lozanic triangle Lozanić triangle Losanitsch's triangle Losanitsch triangle Lossnitsch's triangle
is Wikipage redirect of	Lozanic's triangle Lozanic triangle Lozanić triangle Losanitsch's triangle Losanitsch triangle Lossnitsch's triangle
is foaf:primaryTopic of	wikipedia-en:Lozanić's_triangle

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