cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A118278 Conjectured largest number that is not the sum of three n-gonal numbers, or -1 if there is no largest number.

Original entry on oeis.org

0, -1, 33066, 146858, 273118, -1, 1274522, 2117145, 3613278, -1, 7250758, -1, 12911636, -1, 22655394, 26801303, 25049533, -1, 56922533, 115715602, 81539010, -1, 85105105, -1, 106555658, -1, 233296317, 267370631, 286763923, -1, 358322750
Offset: 3

Views

Author

T. D. Noe, Apr 21 2006

Keywords

Comments

Extensive calculations show that if a(n) >= 0, then every number greater than a(n) can be represented as the sum of three n-gonal numbers. a(3)=0 because every number can be written as the sum of three triangular numbers. When n is a multiple of 4, there is an infinite set of numbers not representable. For n=14, there appears to be a sparse, but infinite, set of numbers not representable.

Links

Crossrefs

Cf. A118279 (number of numbers not representable).
Cf. A003679 (not the sum of three pentagonal numbers).
Cf. A007536 (not the sum of three hexagonal numbers).
Cf. A213523 (not the sum of three heptagonal numbers).
Cf. A213524 (not the sum of three octagonal numbers).
Cf. A213525 (not the sum of three 9-gonal numbers).
Cf. A214419 (not the sum of three 10-gonal numbers).
Cf. A214420 (not the sum of three 11-gonal numbers).
Cf. A214421 (not the sum of three 12-gonal numbers).

Extensions

a(22)-a(33) from Donovan Johnson, Apr 17 2010

A282248 Expansion of (Sum_{k>=0} x^(k*(5*k-3)/2))^7.

Original entry on oeis.org

1, 7, 21, 35, 35, 21, 7, 8, 42, 105, 140, 105, 42, 7, 21, 105, 210, 210, 112, 63, 105, 175, 245, 252, 147, 77, 210, 420, 455, 315, 147, 35, 105, 420, 637, 483, 273, 266, 315, 392, 532, 483, 357, 532, 840, 840, 567, 315, 210, 421, 840, 1050, 777, 462, 497, 707, 882, 917, 735, 525, 889, 1407, 1407, 1050, 770, 525, 630, 1302
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 09 2017

Keywords

Comments

Number of ways to write n as an ordered sum of 7 heptagonal numbers (A000566).
a(n) > 0 for all n >= 0.
Every number is the sum of at most 7 heptagonal numbers.
Every number is the sum of at most k k-gonal numbers (Fermat's polygonal number theorem).

Examples

			a(7) = 8 because we have
[7, 0, 0, 0, 0, 0, 0]
[0, 7, 0, 0, 0, 0, 0]
[0, 0, 7, 0, 0, 0, 0]
[0, 0, 0, 7, 0, 0, 0]
[0, 0, 0, 0, 7, 0, 0]
[0, 0, 0, 0, 0, 7, 0]
[0, 0, 0, 0, 0, 0, 7]
[1, 1, 1, 1, 1, 1, 1]

Links

Crossrefs

Cf. A000566, A045849, A213523, A226252.

Programs

  • Mathematica
    nmax = 67; CoefficientList[Series[Sum[x^(k (5 k - 3)/2), {k, 0, nmax}]^7, {x, 0, nmax}], x]

Formula

G.f.: (Sum_{k>=0} x^(k*(5*k-3)/2))^7.
Showing 1-2 of 2 results.

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