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 A025429 Number of partitions of n into 5 nonzero squares. 17
 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 0, 1, 3, 1, 3, 2, 1, 3, 2, 1, 3, 3, 2, 3, 2, 2, 2, 2, 3, 3, 5, 2, 2, 5, 1, 3, 5, 1, 5, 4, 2, 5, 3, 2, 5, 5, 3, 4, 4, 4, 3, 5, 4, 4, 7, 3, 5, 6, 2, 4, 7, 4, 7, 6, 3, 7, 4, 3, 8, 6, 5, 7, 5, 5, 4, 6, 7, 6, 9, 5, 6, 8, 2, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,21 COMMENTS a(33) is the last zero in this sequence, cf the link to stackexchange.com and also A080673(n) for the largest index k with a(k)=n. - M. F. Hasler, May 30 2014 First occurrence of k beginning with 0: 0, 5, 20, 29, 62, 53, 80, 77, 91, 101, ..., (A080654). - Robert G. Wilson v, May 30 2014 LINKS M. F. Hasler, Table of n, a(n) for n = 0..10000 H. v. Eitzen, in reply to user James47, What is the largest integer with only one representation as a sum of five nonzero squares? on stackexchange.com, May 2014 FORMULA a(n) = [x^n y^5] Product_{k>=1} 1/(1 - y*x^(k^2)). - Ilya Gutkovskiy, Apr 19 2019 a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-1)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} A010052(i) * A010052(j) * A010052(k) * A010052(l) * A010052(n-i-j-k-l). - Wesley Ivan Hurt, Apr 19 2019 MAPLE b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),       `if`(i<1 or t<1, 0, b(n, i-1, t)+       `if`(i^2>n, 0, b(n-i^2, i, t-1))))     end: a:= n-> b(n, isqrt(n), 5): seq(a(n), n=0..120);  # Alois P. Heinz, May 30 2014 MATHEMATICA f[n_] := Block[{c = Range@ Sqrt@ n^2}, Length@ IntegerPartitions[n, {5}, c]]; Array[f, 105, 0] (* Robert G. Wilson v, May 30 2014 *) b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t==0, 1, 0], If[i<1 || t<1, 0, b[n, i-1, t] + If[i^2>n, 0, b[n-i^2, i, t-1]]]]; a[n_] := b[n, Sqrt[n] // Floor, 5]; Table[a[n], {n, 0, 120}] (* Jean-François Alcover, Oct 12 2015, after Alois P. Heinz *) PROG (PARI)  A025429(n)=sum(d=sqrtint(max(n, 5)\5), sqrtint(max(n-4, 0)), nn=n-d^2; sum(a=sqrtint(max(nn-d^2, 4)\4), min(sqrtint(max(nn-3, 0)), d), sum(b=sqrtint((nn-a^2)\3-1)+1, min(sqrtint(nn-a^2-2), a), sum(c=sqrtint((t=nn-a^2-b^2)\2-1)+1, min(sqrtint(t-1), b), issquare(t-c^2) )))) \\ M. F. Hasler, May 30 2014 CROSSREFS Column k=5 of A243148. Sequence in context: A261794 A098744 A273975 * A325561 A076250 A231425 Adjacent sequences:  A025426 A025427 A025428 * A025430 A025431 A025432 KEYWORD nonn,easy,look AUTHOR STATUS approved

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Last modified June 15 16:13 EDT 2019. Contains 324142 sequences. (Running on oeis4.)