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Search: id:A139309
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| A139309 |
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Array by antidiagonals, sum of non-k-gonal numbers between consecutive k-gonal numbers. |
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+0
1
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| 0, 0, 2, 0, 5, 9, 0, 9, 26, 24, 0, 14, 51, 75, 50, 0, 20, 84, 153, 164, 90, 0, 27, 125, 258, 342, 305, 147, 0, 35, 174, 390, 584, 645, 510, 224, 0, 44, 231, 549, 890, 1110, 1089, 791, 324, 0, 54, 296, 735, 1260, 1700, 1884, 1701, 1160, 450, 0, 65, 369, 948, 1694
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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The n=1 column is A000096(k) = n*(n+3)/2. The k=3 row is the sum of nontriangular numbers between successive triangular numbers (A006002) = the sum of n consecutive integers beginning with (n-th triangular number)+1 = (n*(n+1)^2)/2. The k=4 row is the sum of non-squares between successive squares (A048395) = 2*n^3 + 2*n^2 + n. The k=5 row is the sum of non-pentagonal numbers between successive pentagonal numbers. The k-th row is the sum of non-k-gonal numbers between successive k-gonal numbers. Each column is a quadratic sequence. Each row is a cubic sequence.
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FORMULA
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T(k,n) = n(k-2)((k-2)n^2+1+2n)/2. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 12 2008
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EXAMPLE
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The array begins:
========================================================================
...|.n=0.|.n=1.|.n=2.|.n=3.|.n=4.|.n=5.|.n=6.|.n=7.|.n=8.|.n=9.|.in.OEIS
====|=====|=====|=====|=====|=====|=====|=====|=====|=====|=====|========
k=3.|..0..|..2..|..9..|..24.|..50.|..90.|.147.|.224.|.324.|.450.|.A006002
k=4.|..0..|..5..|.26..|..75.|.164.|.305.|.510.|.791.|1160.|1629.|.A048395
k=5.|..0..|..9..|.51..|.153.|.342.|.645.|1089.|...................not.yet
k=6.|..0..|.14..|.84..|.258.|.584.|...............................not.yet
k=7.|..0..|.20..|125..|.390.|.....................................not.yet
k=8.|..0..|.27..|174..|...........................................not.yet
k=9.|..0..|.35..|231..|...........................................not.yet
k=10|..0..|.44..|296..|...........................................not.yet
========================================================================
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MAPLE
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A139309 := proc(k, n) n*(k-2)*((k-2)*n^2+1+2*n)/2 ; end: for d from 3 to 16 do for n from 0 to d-3 do printf("%d, ", A139309(d-n, n)) ; od: od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 12 2008
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CROSSREFS
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Cf. A000027, A000096, A006002, A048395.
Sequence in context: A011122 A085009 A011435 this_sequence A011014 A002976 A080901
Adjacent sequences: A139306 A139307 A139308 this_sequence A139310 A139311 A139312
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 07 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 12 2008
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