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A167661 Number of partitions of n into odd squares. 11
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 11, 11, 12, 12, 13, 13, 13, 13, 14, 15, 15, 16, 16, 17, 17, 17, 17, 18, 19, 19, 20, 20, 21, 21, 22, 23, 24, 25, 25, 26, 26, 28, 28, 29, 30, 31 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,10
COMMENTS
A167662 and A167663 give record values and where they occur: A167662(n)=a(A167663(n)) and a(m) < A167662(n) for m < A167663(n).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from R. Zumkeller)
FORMULA
a(n) = f(n,1,8) with f(x,y,z) = if x<y then 0^x else f(x-y,y,z)+f(x,y+z,z+8).
G.f.: G = 1/Product_{i>=1}(1-x^{(2i-1)^2}). - Emeric Deutsch , Jan 26 2016
a(n) ~ exp(3 * Pi^(1/3) * Zeta(3/2)^(2/3) * n^(1/3) / 4) * Zeta(3/2)^(1/3) / (4 * sqrt(3) * Pi^(1/3) * n^(5/6)). - Vaclav Kotesovec, Sep 18 2017
EXAMPLE
a(10)=#{9+1,1+1+1+1+1+1+1+1+1+1}=2;
a(20)=#{9+9+1+1,9+1+1+1+1+1+1+1+1+1+1+1,20x1}=3;
a(30)=#{25+1+1+1+1+1,9+9+9+1+1+1,9+9+12x1,9+21x1,30x1}=5.
MAPLE
g := 1/mul(1-x^((2*i-1)^2), i = 1 .. 150): gser := series(g, x = 0, 105): seq(coeff(gser, x, n), n = 0 .. 100);
MATHEMATICA
nmax = 100; CoefficientList[Series[Product[1/(1 - x^((2*k-1)^2)), {k, 1, Floor[Sqrt[nmax]/2] + 1}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 18 2017 *)
CROSSREFS
Sequence in context: A279951 A279224 A167383 * A187187 A300358 A102682
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 08 2009
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)