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A151667 Number of partitions of n into distinct powers of 5.

%I A151667 #17 Feb 24 2021 02:48:18
%S A151667 1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,
%T A151667 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A151667 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A151667 Number of partitions of n into distinct powers of 5.
%H A151667 Alois P. Heinz, <a href="/A151667/b151667.txt">Table of n, a(n) for n = 0..15625</a>
%H A151667 David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
%H A151667 N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%F A151667 G.f.: Prod_{k >= 0 } (1+x^(5^k)). Exponents give A033042.
%F A151667 G.f. A(x) satisfies: A(x) = (1 + x) * A(x^5). - _Ilya Gutkovskiy_, Aug 12 2019
%t A151667 m = 130; A[_] = 1;
%t A151667 Do[A[x_] = (1+x) A[x^5] + O[x]^m // Normal, {m}];
%t A151667 CoefficientList[A[x], x] (* _Jean-François Alcover_, Oct 19 2019 *)
%Y A151667 For generating functions Prod_{k>=0} (1+a*x^(b^k)) for the following values of (a,b) see: (1,2) A000012 and A000027, (1,3) A039966 and A005836, (1,4) A151666 and A000695, (1,5) A151667 and A033042, (2,2) A001316, (2,3) A151668, (2,4) A151669, (2,5) A151670, (3,2) A048883, (3,3) A117940, (3,4) A151665, (3,5) A151671, (4,2) A102376, (4,3) A151672, (4,4) A151673, (4,5) A151674.
%Y A151667 Cf. A039966, A151666, A033042.
%K A151667 nonn
%O A151667 0,1
%A A151667 _N. J. A. Sloane_, May 30 2009