OFFSET
0,5
COMMENTS
Sum of products of terms in all partitions of n into squares (A000290).
FORMULA
G.f.: Product_{k>=1} 1/(1 - k^2*x^(k^2)).
From Vaclav Kotesovec, Feb 09 2017: (Start)
a(n) ~ c * 2^(n/2), where:
c = 1.84902025727376837058629436557644856279088... if n == 0 (mod 4),
c = 1.74739571210218418633067606853005648684028... if n == 1 (mod 4),
c = 1.41060067910504703778072732362810764186990... if n == 2 (mod 4),
c = 1.06705333199321743850009229910087278853310... if n == 3 (mod 4).
(End)
EXAMPLE
a(8) = 21 because we have [4, 4], [4, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], 4*4 = 16, 4*1*1*1*1 = 4, 1*1*1*1*1*1*1*1 = 1 and 16 + 4 + 1 = 21.
MATHEMATICA
nmax = 44; CoefficientList[Series[Product[1/(1 - k^2 x^k^2), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 09 2017
STATUS
approved