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 A045852 Number of nonnegative solutions of x1^2 + x2^2 + ... + x10^2 = n. 5
 1, 10, 45, 120, 220, 342, 570, 960, 1350, 1640, 2191, 3240, 4200, 4720, 5760, 7920, 9865, 10620, 11965, 15600, 19332, 20550, 22200, 28080, 34200, 35582, 37395, 45720, 54600, 56970, 59460, 71040, 84330, 87090, 88195, 104040, 123200, 125710, 126540, 148560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..2000 from T. D. Noe) FORMULA Coefficient of q^n in (1 + q + q^4 + q^9 + q^16 + q^25 + q^36 + q^49 + q^64 + ...)^10. G.f.: ((1 + theta_3(x)) / 2)^10. - Ilya Gutkovskiy, Feb 10 2021 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:= b(n, 10): seq(a(n), n=0..40); # Alois P. Heinz, Feb 10 2021 MATHEMATICA Take[CoefficientList[Expand[(Total[x^Range[0, 5]^2])^10], x], 50] (* Harvey P. Dale, May 20 2011 *) PROG (Ruby) def mul(f_ary, b_ary, m) s1, s2 = f_ary.size, b_ary.size ary = Array.new(s1 + s2 - 1, 0) (0..s1 - 1).each{|i| (0..s2 - 1).each{|j| ary[i + j] += f_ary[i] * b_ary[j] } } ary[0..m] end def power(ary, n, m) if n == 0 a = Array.new(m + 1, 0) a[0] = 1 return a end k = power(ary, n >> 1, m) k = mul(k, k, m) return k if n & 1 == 0 return mul(k, ary, m) end def A(k, n) ary = Array.new(n + 1, 0) (0..Math.sqrt(n).to_i).each{|i| ary[i * i] = 1} power(ary, k, n) end p A(10, 100) # Seiichi Manyama, May 28 2017 CROSSREFS Cf. A010052, A045847. Sequence in context: A010926 A229395 A306965 * A226450 A105938 A342254 Adjacent sequences: A045849 A045850 A045851 * A045853 A045854 A045855 KEYWORD nonn AUTHOR N. J. A. Sloane STATUS approved

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Last modified May 21 22:16 EDT 2024. Contains 372741 sequences. (Running on oeis4.)