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A341400
Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_5)^2 <= n.
6
1, 6, 16, 26, 36, 57, 87, 107, 122, 157, 207, 247, 277, 322, 392, 452, 482, 537, 637, 717, 773, 863, 973, 1053, 1113, 1203, 1343, 1473, 1553, 1668, 1858, 1998, 2053, 2173, 2373, 2543, 2673, 2818, 3018, 3218, 3338, 3483, 3753, 3973, 4113, 4344, 4634, 4834, 4944, 5139, 5449
OFFSET
0,2
COMMENTS
Partial sums of A038671.
FORMULA
G.f.: (1 + theta_3(x))^5 / (32 * (1 - x)).
a(n^2) = A055404(n).
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1, `if`(n<0 or k<1, 0,
b(n, k-1)+add(b(n-j^2, k-1), j=1..isqrt(n))))
end:
a:= proc(n) option remember; b(n, 5)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..50); # Alois P. Heinz, Feb 10 2021
MATHEMATICA
nmax = 50; CoefficientList[Series[(1 + EllipticTheta[3, 0, x])^5/(32 (1 - x)), {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 10 2021
STATUS
approved