A248801 Number of sets of nonzero squares with sum <= n

1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 6, 7, 8, 8, 9, 10, 10, 10, 11, 12, 12, 12, 12, 14, 16, 16, 16, 18, 20, 20, 20, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 30, 30, 32, 34, 34, 34, 36, 39, 40, 41, 43, 45, 46, 47, 48, 49, 50, 50, 52, 55, 56, 57, 61, 64, 64, 65

Offset

0,2

Comments

Partial sums of A033461.

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

G.f.: (1-x)^(-1) * product(k>=1, 1 + x^(k^2)).

Example

For n=5 the sets are {}, {1^2}, {2^2}, {1^2, 2^2} so a(5) = 4.

Maple

N:= 200: # to get a(0) to a(N)
g:= (1-x)^(-1)*mul(1 + x^(m^2), m=1 .. floor(sqrt(N))):
S:= series(g, x, N+1):
seq(coeff(S, x, j), j=0..N);

Mathematica

CoefficientList[Series[(1 - x)^(-1) Product[1 + x^(k^2), {k, 50}], {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2014 *)
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i^2>n, 0, b[n-i^2, i-1]]]]; Table[b[n, Floor[Sqrt[n]]], {n, 0, 100}] // Accumulate (* Jean-François Alcover, Apr 17 2019, after Alois P. Heinz in A033461 *)

Crossrefs

Cf. A033461.

Sequence in context: A087816 A072000 A157477 * A006949 A359536 A194814

Adjacent sequences: A248798 A248799 A248800 * A248802 A248803 A248804

Keyword

nonn

Author

Robert Israel, Oct 14 2014

Status

approved