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
Keywords
Examples
a(26) = 3 because 26=25+1=5+5+5+5+5+1=5+5+5+5+1+1+1+1+1+1.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..15625
Crossrefs
Programs
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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 *)
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