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

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, 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, 1, 1, 2, 2, 1, 1, 1, 3, 3, 2, 2, 2, 4, 4, 2, 2, 2, 3, 3, 1, 1, 1, 2, 2

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..15625

Formula

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

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

Example

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

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<0, 0,
      add(b(n-j*5^i, i-1), j=0..min(6, n/5^i))))
    end:
a:= n-> b(n, ilog[5](n)):
seq(a(n), n=0..120);  # Alois P. Heinz, May 01 2018

Mathematica

m = 100; A[_] = 1;
Do[A[x_] = Total[x^Range[0, 6]] A[x^5] + O[x]^m // Normal, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Oct 19 2019 *)

Crossrefs

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).

Cf. A277873.

Sequence in context: A316089 A000999 A175921 * A025451 A184257 A365721

Adjacent sequences: A303825 A303826 A303827 * A303829 A303830 A303831

Keyword

nonn

Author

Seiichi Manyama, May 01 2018

Status

approved