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%I #23 Oct 06 2019 12:34:00
%S 1,1,1,1,2,2,1,1,2,2,1,1,2,2,1,1,3,3,2,2,4,4,2,2,3,3,1,1,2,2,1,1,3,3,
%T 2,2,4,4,2,2,3,3,1,1,2,2,1,1,3,3,2,2,4,4,2,2,3,3,1,1,2,2,1,1,4,4,3,3,
%U 6,6,3,3,5,5,2,2,4,4,2,2,6,6,4,4,8,8,4,4,6,6
%N Number of ways of writing n as a sum of powers of 4, each power being used at most 5 times.
%H Alois P. Heinz, <a href="/A303827/b303827.txt">Table of n, a(n) for n = 0..16383</a>
%F G.f.: Product_{k>=0} (1-x^(6*4^k))/(1-x^(4^k)).
%F G.f. A(x) satisfies: A(x) = (1 + x + x^2 + x^3 + x^4 + x^5) * A(x^4). - _Ilya Gutkovskiy_, Jul 09 2019
%e a(17) = 3 because 17=16+1=4+4+4+4+1=4+4+4+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*4^i, i-1), j=0..min(5, n/4^i))))
%p end:
%p a:= n-> b(n, ilog[4](n)):
%p seq(a(n), n=0..120); # _Alois P. Heinz_, May 01 2018
%t m = 100; A[_] = 1;
%t Do[A[x_] = (1+x+x^2+x^3+x^4+x^5) * A[x^4] + O[x]^m // Normal, {m}];
%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Oct 06 2019, after _Ilya Gutkovskiy_ *)
%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), this sequence (b=4), A303828 (b=5).
%Y Cf. A277872.
%K nonn,look
%O 0,5
%A _Seiichi Manyama_, May 01 2018
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