A341399 Number of integer solutions to (x_1)^2 + (x_2)^2 + ... + (x_10)^2 <= n.

1, 21, 201, 1161, 4541, 12965, 29285, 58085, 110105, 198765, 327829, 503509, 765589, 1152509, 1642109, 2243069, 3083569, 4221529, 5551949, 7115789, 9166133, 11777333, 14763893, 18121973, 22316213, 27634481, 33512921, 39812441, 47674841, 57294401, 67510721, 78592961

Offset

0,2

Comments

Partial sums of A000144.

Links

Table of n, a(n) for n=0..31.

Index entries for sequences related to sums of squares

Formula

G.f.: theta_3(x)^10 / (1 - x).

a(n^2) = A055416(n).

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, `if`(n<0 or k<1, 0,
      b(n, k-1)+2*add(b(n-j^2, k-1), j=1..isqrt(n))))
    end:
a:= proc(n) option remember; b(n, 10)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..31);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 31; CoefficientList[Series[EllipticTheta[3, 0, x]^10/(1 - x), {x, 0, nmax}], x]
Table[SquaresR[10, n], {n, 0, 31}] // Accumulate

Crossrefs

Cf. A000122, A000144, A001650, A046895, A055409, A055416, A057655, A117609, A122510, A175360, A175361, A302860, A341396, A341397, A341398.

Sequence in context: A221126 A239418 A337897 * A125384 A126542 A297906

Adjacent sequences: A341396 A341397 A341398 * A341400 A341401 A341402

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 10 2021

Status

approved