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. 4-5].

LINKS

Zhi-Wei 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

KEYWORD

nonn,easy

AUTHOR

Robert G. Wilson v, May 14 2014

STATUS

approved