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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 A275656

Adjacent sequences:  A303825 A303826 A303827 * A303829 A303830 A303831

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 01 2018

STATUS

approved

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Last modified May 26 02:56 EDT 2020. Contains 334613 sequences. (Running on oeis4.)