cp's OEIS Frontend

A045849 Number of nonnegative solutions of x1^2 + x2^2 + ... + x7^2 = n.

%I A045849 #33 Aug 26 2019 08:05:15
%S A045849 1,7,21,35,42,63,112,141,126,154,259,315,280,308,462,567,497,462,693,
%T A045849 910,798,749,1078,1281,1092,1043,1407,1715,1576,1449,1946,2422,2016,
%U A045849 1687,2429,3045,2604,2345,3066
%N A045849 Number of nonnegative solutions of x1^2 + x2^2 + ... + x7^2 = n.
%H A045849 Seiichi Manyama, <a href="/A045849/b045849.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..2000 from T. D. Noe)
%H A045849 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A045849 Coefficient of q^n in (1 + q + q^4 + q^9 + q^16 + q^25 + q^36 + q^49 + q^64 + ...)^7.
%F A045849 G.f.: (1 + theta_3(q))^7/128, where theta_3() is the Jacobi theta function. - _Ilya Gutkovskiy_, Aug 08 2018
%t A045849 (1 + EllipticTheta[3, 0, q])^7/128 + O[q]^50 // CoefficientList[#, q]& (* _Jean-François Alcover_, Aug 26 2019 *)
%o A045849 (PARI) seq(n)=Vec((sum(k=0, sqrtint(n), x^(k^2)) + O(x*x^n))^7) \\ _Andrew Howroyd_, Aug 08 2018
%o A045849 (Ruby)
%o A045849 def mul(f_ary, b_ary, m)
%o A045849   s1, s2 = f_ary.size, b_ary.size
%o A045849   ary = Array.new(s1 + s2 - 1, 0)
%o A045849   (0..s1 - 1).each{|i|
%o A045849     (0..s2 - 1).each{|j|
%o A045849       ary[i + j] += f_ary[i] * b_ary[j]
%o A045849     }
%o A045849   }
%o A045849   ary[0..m]
%o A045849 end
%o A045849 def power(ary, n, m)
%o A045849   if n == 0
%o A045849     a = Array.new(m + 1, 0)
%o A045849     a[0] = 1
%o A045849     return a
%o A045849   end
%o A045849   k = power(ary, n >> 1, m)
%o A045849   k = mul(k, k, m)
%o A045849   return k if n & 1 == 0
%o A045849   return mul(k, ary, m)
%o A045849 end
%o A045849 def A(k, n)
%o A045849   ary = Array.new(n + 1, 0)
%o A045849   (0..Math.sqrt(n).to_i).each{|i| ary[i * i] = 1}
%o A045849   power(ary, k, n)
%o A045849 end
%o A045849 p A(7, 100) # _Seiichi Manyama_, May 28 2017
%Y A045849 Cf. A010052, A038671, A045847.
%K A045849 nonn
%O A045849 0,2
%A A045849 _N. J. A. Sloane_