A288631 Numbers that are the sum of two nonzero square pyramidal numbers (A000330).

2, 6, 10, 15, 19, 28, 31, 35, 44, 56, 60, 69, 85, 92, 96, 105, 110, 121, 141, 145, 146, 154, 170, 182, 195, 205, 209, 218, 231, 234, 259, 280, 286, 290, 295, 299, 315, 340, 344, 376, 386, 390, 399, 408, 415, 425, 440, 476, 489, 507, 511, 520, 525, 536, 561, 570, 589, 597, 646, 651, 655, 664, 670, 680

Offset: 1

Author

Ilya Gutkovskiy, Jun 12 2017

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Square Pyramidal Number
• Index to sequences related to pyramidal numbers

Crossrefs

Cf. A000330, A000404, A020756, A051533, A102795.

Programs

Maple

M:= 20: # to get all terms <= A000330(M)
sqp:= [seq(k*(k+1)*(2*k+1)/6, k=1..M)]:
sort(convert(select(`<=`, {seq(seq(sqp[i]+sqp[j], j=1..i),i=1..M-1)},sqp[M]),list)); # Robert Israel, Jun 12 2017

Mathematica

nmax = 700; f[x_] := Sum[x^(k (k + 1) (2 k + 1)/6), {k, 1, 20}]^2; Exponent[#, x] & /@ List @@ Normal[Series[f[x], {x, 0, nmax}]]