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A139309 Array by antidiagonals, sum of non-k-gonal numbers between consecutive k-gonal numbers. 1
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; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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 nonsquares 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.

LINKS

Table of n, a(n) for n=0..59.

FORMULA

T(k,n) = n(k-2)((k-2)n^2+1+2n)/2. - R. J. Mathar, Jun 12 2008

EXAMPLE

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

========================================================================

MAPLE

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, Jun 12 2008

CROSSREFS

Cf. A000027, A000096, A006002, A048395.

Sequence in context: A085009 A192883 A011435 * A264299 A243445 A227569

Adjacent sequences:  A139306 A139307 A139308 * A139310 A139311 A139312

KEYWORD

easy,nonn,tabl

AUTHOR

Jonathan Vos Post, Jun 07 2008

EXTENSIONS

More terms from R. J. Mathar, Jun 12 2008

STATUS

approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)