login
A280863
Expansion of 1/(1 - Sum_{k>=0} x^((2*k+1)^2)).
5
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 19, 24, 30, 37, 45, 55, 66, 79, 95, 115, 140, 171, 209, 255, 312, 381, 464, 564, 685, 832, 1011, 1229, 1494, 1818, 2214, 2697, 3285, 4000, 4869, 5926, 7211, 8772, 10670, 12980, 15793, 19219, 23391, 28470, 34653, 42179, 51336, 62475, 76025, 92510
OFFSET
0,10
COMMENTS
Number of compositions (ordered partitions) of n into odd squares (A016754).
FORMULA
G.f.: 1/(1 - Sum_{k>=0} x^((2*k+1)^2)).
EXAMPLE
a(12) = 5 because we have [9, 1, 1, 1], [1, 9, 1, 1], [1, 1, 9, 1], [1, 1, 1, 9] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
MATHEMATICA
nmax = 63; CoefficientList[Series[1/(1 - Sum[x^(2 k + 1)^2, {k, 0, nmax}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 09 2017
STATUS
approved