login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of ways of writing n as a sum of powers of 5, each power being used at most 6 times.
2

%I #18 Oct 19 2019 10:11:20

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

%H Alois P. Heinz, <a href="/A303828/b303828.txt">Table of n, a(n) for n = 0..15625</a>

%F G.f.: Product_{k>=0} (1-x^(7*5^k))/(1-x^(5^k)).

%F 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 a(26) = 3 because 26=25+1=5+5+5+5+5+1=5+5+5+5+1+1+1+1+1+1.

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<0, 0,

%p add(b(n-j*5^i, i-1), j=0..min(6, n/5^i))))

%p end:

%p a:= n-> b(n, ilog[5](n)):

%p seq(a(n), n=0..120); # _Alois P. Heinz_, May 01 2018

%t m = 100; A[_] = 1;

%t Do[A[x_] = Total[x^Range[0, 6]] A[x^5] + O[x]^m // Normal, {m}];

%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Oct 19 2019 *)

%Y 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 Cf. A277873.

%K nonn

%O 0,6

%A _Seiichi Manyama_, May 01 2018