

A242443


Number of ways of writing n, a positive integer, as an unordered sum of a triangular number (A000217), an even square (A016742) and a generalized pentagonal number (A001318).


2



1, 1, 2, 1, 2, 3, 3, 4, 1, 4, 3, 4, 2, 2, 5, 3, 5, 3, 5, 4, 5, 7, 3, 4, 4, 6, 6, 4, 6, 3, 5, 7, 6, 4, 1, 7, 7, 6, 5, 6, 9, 5, 7, 7, 8, 6, 8, 4, 6, 6, 7, 9, 4, 10, 3, 6, 9, 7, 8, 5, 9, 7, 6, 7, 5, 11, 9, 7, 3, 7, 12, 13, 7, 7, 6, 9, 11, 6, 11, 8, 7, 10, 10, 8, 8, 8, 11, 5, 8, 5, 8, 11, 10, 10, 6, 14, 10, 6, 7, 7
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OFFSET

1,3


COMMENTS

It is conjectured (1.1) and then proved by theorem 1.2 that all positive integers can be so represented [Sun, pp. 45].


LINKS

Table of n, a(n) for n=1..100.
ZhiWei Sun, On Universal Sums Of Polygonal Numbers, arXiv:0905.0635v18 [math.NT] 26 Oct 2011


MATHEMATICA

planeFigurative[n_, r_] := pf[n, r] = (n  2) Binomial[r, 2] + r; s = Sort@ Table[ planeFigurative[3, i] + planeFigurative[3, j] + planeFigurative[3, k], {i, 0, 14}, {j, 0, 10, 2}, {k, 8, 8}]; Table[ Count[s, n], {n, 0, 50}]


CROSSREFS

Cf. A002636, A115288, A160324, A160325, A160326, A240088, A242442.
Sequence in context: A100405 A081366 A129636 * A214154 A048219 A087188
Adjacent sequences: A242440 A242441 A242442 * A242444 A242445 A242446


KEYWORD

nonn,easy


AUTHOR

Robert G. Wilson v, May 14 2014


STATUS

approved



