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A242442 Number of ways of writing n, a positive integer, as an unordered sum of a triangular number (A000217), an odd square (A016754) and a pentagonal number (A000326). 2
1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 2, 3, 2, 2, 2, 4, 2, 0, 2, 2, 2, 2, 3, 4, 2, 3, 3, 2, 4, 3, 5, 2, 2, 3, 2, 4, 5, 4, 1, 3, 3, 4, 1, 2, 3, 5, 5, 1, 3, 5, 5, 4, 4, 4, 4, 2, 5, 4, 5, 4, 5, 4, 2, 5, 4, 4, 4, 4, 2, 4, 5, 5, 2, 2, 6, 5, 4, 2, 4, 6, 7, 7, 2, 3, 5, 6, 5, 5, 5, 2, 5, 9, 3, 5, 2, 8, 6, 1, 8, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It is conjectured that only 18 cannot be so represented. See Sun, p. 4, Remark 1.2 (b).

LINKS

Table of n, a(n) for n=1..100.

Zhi-Wei Sun, On Universal Sums Of Polygonal Numbers, arXiv:0905.0635v18 [math.NT] 26 Oct 2011

MATHEMATICA

planeFigurative[n_, r_] := (n - 2) Binomial[r, 2] + r; s = Sort@ Flatten@ Table[ planeFigurative[3, i] + planeFigurative[4, j] + planeFigurative[5, k], {i, 0, 20}, {j, 1, 11, 2}, {k, 0, 8}]; Table[ Count[s, n], {n, 0, 104}]

CROSSREFS

Cf. A002636, A115288, A160324, A160325, A160326, A240088, A242443.

Sequence in context: A025883 A111335 A345238 * A163768 A327659 A327519

Adjacent sequences:  A242439 A242440 A242441 * A242443 A242444 A242445

KEYWORD

nonn,easy

AUTHOR

Robert G. Wilson v, May 14 2014

STATUS

approved

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Last modified January 24 19:03 EST 2022. Contains 350565 sequences. (Running on oeis4.)