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A289520
Numbers that are the sum of distinct squares of triangular numbers (A000537).
0
0, 1, 9, 10, 36, 37, 45, 46, 100, 101, 109, 110, 136, 137, 145, 146, 225, 226, 234, 235, 261, 262, 270, 271, 325, 326, 334, 335, 361, 362, 370, 371, 441, 442, 450, 451, 477, 478, 486, 487, 541, 542, 550, 551, 577, 578, 586, 587, 666, 667, 675, 676, 702, 703, 711, 712, 766, 767, 775, 776, 784, 785, 793, 794
OFFSET
1,3
FORMULA
Exponents in expansion of Product_{k>=1} (1 + x^(k*(k+1)/2)^2).
EXAMPLE
37 is in the sequence because 37 = 1 + 36 = 1^2 + (1 + 2 + 3)^2 = 1^3 + 1^3 + 2^3 + 3^3.
MATHEMATICA
max = 800; f[x_] := Product[1 + x^(k (k + 1)/2)^2, {k, 1, 10}]; Exponent[#, x] & /@ List @@ Normal[Series[f[x], {x, 0, max}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 14 2017
STATUS
approved