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 A045849 Number of nonnegative solutions of x1^2 + x2^2 + ... + x7^2 = n. 6
 1, 7, 21, 35, 42, 63, 112, 141, 126, 154, 259, 315, 280, 308, 462, 567, 497, 462, 693, 910, 798, 749, 1078, 1281, 1092, 1043, 1407, 1715, 1576, 1449, 1946, 2422, 2016, 1687, 2429, 3045, 2604, 2345, 3066 (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) Index entries for sequences related to sums of squares FORMULA Coefficient of q^n in (1 + q + q^4 + q^9 + q^16 + q^25 + q^36 + q^49 + q^64 + ...)^7. G.f.: (1 + theta_3(q))^7/128, where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 08 2018 MATHEMATICA (1 + EllipticTheta[3, 0, q])^7/128 + O[q]^50 // CoefficientList[#, q]& (* Jean-François Alcover, Aug 26 2019 *) PROG (PARI) seq(n)=Vec((sum(k=0, sqrtint(n), x^(k^2)) + O(x*x^n))^7) \\ Andrew Howroyd, Aug 08 2018 (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(7, 100) # Seiichi Manyama, May 28 2017 CROSSREFS Cf. A010052, A038671, A045847. Sequence in context: A282248 A282349 A356454 * A031008 A147587 A208543 Adjacent sequences: A045846 A045847 A045848 * A045850 A045851 A045852 KEYWORD nonn AUTHOR N. J. A. Sloane STATUS approved

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Last modified December 6 16:13 EST 2023. Contains 367612 sequences. (Running on oeis4.)