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).

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

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