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 A025431 Number of partitions of n into 7 nonzero squares. 18
 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 2, 3, 1, 1, 4, 2, 3, 4, 1, 4, 3, 1, 5, 4, 3, 4, 4, 4, 3, 4, 4, 5, 7, 3, 5, 7, 3, 5, 8, 4, 7, 7, 4, 8, 6, 3, 9, 10, 6, 8, 8, 7, 7, 8, 8, 9, 11, 7, 9, 12, 6, 8, 15, 8, 12, 12, 7, 15, 10, 8, 16, 13, 11, 13, 13, 12, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,23 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA a(n) = [x^n y^7] Product_{k>=1} 1/(1 - y*x^(k^2)). - Ilya Gutkovskiy, Apr 19 2019 a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} A010052(i) * A010052(j) * A010052(k) * A010052(l) * A010052(m) * A010052(o) A010052(n-i-j-k-l-m-o). - 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), 7): seq(a(n), n=0..120);  # Alois P. Heinz, May 30 2014 MATHEMATICA 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, 7]; Table[a[n], {n, 0, 120}] (* Jean-François Alcover, Apr 30 2018, after Alois P. Heinz *) CROSSREFS Column k=7 of A243148. Sequence in context: A340101 A049847 A255274 * A161070 A161109 A161044 Adjacent sequences:  A025428 A025429 A025430 * A025432 A025433 A025434 KEYWORD nonn,look AUTHOR STATUS approved

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Last modified August 8 09:40 EDT 2022. Contains 356009 sequences. (Running on oeis4.)