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A303828 Number of ways of writing n as a sum of powers of 5, each power being used at most 6 times.

%I A303828 #18 Oct 19 2019 10:11:20
%S A303828 1,1,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,3,3,2,2,2,4,4,2,2,
%T A303828 2,3,3,1,1,1,2,2,1,1,1,2,2,1,1,1,3,3,2,2,2,4,4,2,2,2,3,3,1,1,1,2,2,1,
%U A303828 1,1,2,2,1,1,1,3,3,2,2,2,4,4,2,2,2,3,3,1,1,1,2,2
%N A303828 Number of ways of writing n as a sum of powers of 5, each power being used at most 6 times.
%H A303828 Alois P. Heinz, <a href="/A303828/b303828.txt">Table of n, a(n) for n = 0..15625</a>
%F A303828 G.f.: Product_{k>=0} (1-x^(7*5^k))/(1-x^(5^k)).
%F A303828 G.f. A(x) satisfies: A(x) = (1 + x + x^2 + x^3 + x^4 + x^5 + x^6) * A(x^5). - _Ilya Gutkovskiy_, Jul 09 2019
%e A303828 a(26) = 3 because 26=25+1=5+5+5+5+5+1=5+5+5+5+1+1+1+1+1+1.
%p A303828 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<0, 0,
%p A303828       add(b(n-j*5^i, i-1), j=0..min(6, n/5^i))))
%p A303828     end:
%p A303828 a:= n-> b(n, ilog[5](n)):
%p A303828 seq(a(n), n=0..120);  # _Alois P. Heinz_, May 01 2018
%t A303828 m = 100; A[_] = 1;
%t A303828 Do[A[x_] = Total[x^Range[0, 6]] A[x^5] + O[x]^m // Normal, {m}];
%t A303828 CoefficientList[A[x], x] (* _Jean-François Alcover_, Oct 19 2019 *)
%Y A303828 Number of ways of writing n as a sum of powers of b, each power being used at most b+1 times: A117535 (b=3), A303827 (b=4), this sequence (b=5).
%Y A303828 Cf. A277873.
%K A303828 nonn
%O A303828 0,6
%A A303828 _Seiichi Manyama_, May 01 2018