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 A045854 Number of nonnegative solutions of x1^2 + x2^2 + ... + x24^2 = n. 1
 1, 24, 276, 2024, 10650, 43056, 140668, 388608, 948267, 2121176, 4448292, 8811024, 16535160, 29632464, 51256788, 86069680, 140300001, 222302544, 344353516, 523941288, 782700672, 1146771168, 1653111384 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES Coefficient of q^n in (1 + q + q^4 + q^9 + q^16 + q^25 + q^36 + q^49 + q^64 + ...)^24. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..2000 from T. D. Noe) 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(24, 100) # Seiichi Manyama, May 28 2017 CROSSREFS Cf. A010052, A045847. Sequence in context: A000915 A006665 A010940 * A014809 A007191 A097340 Adjacent sequences:  A045851 A045852 A045853 * A045855 A045856 A045857 KEYWORD nonn AUTHOR STATUS approved

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