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A078537 Number of partitions of 4^n into powers of 4 (without regard to order).

%I A078537 #21 Nov 28 2017 11:42:57
%S A078537 1,2,6,46,1086,79326,18583582,14481808030,38559135542174,
%T A078537 357934565638890910,11766678027350761752990,
%U A078537 1387043469046575118555443614,592264246356176268834689653440926,923812464024548700407122072128655860126,5301247577915139769925461060755690116740047262
%N A078537 Number of partitions of 4^n into powers of 4 (without regard to order).
%C A078537 Conjecture: a(n) = sum of the n-th row of lower triangular matrix A078536.
%H A078537 Alois P. Heinz, <a href="/A078537/b078537.txt">Table of n, a(n) for n = 0..60</a>
%F A078537 a(n) = coefficient of x^(4^n) in power series expansion of 1/[(1-x)(1-x^4)(1-x^16)...(1-x^(4^k))...].
%e A078537 a(2) = 6 since partitions of 4^2 into powers of 4 are: [16], [4,4,4,4], [4,4,4,1,1,1,1], [4,4,1,1,1,1,1,1,1,1], [4,1,1,1,1,1,1,1,1,1,1,1,1], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1].
%t A078537 a[0] = 1; a[n_] := a[n] = a[n - 1] + a[Floor[n/4]]; b = Table[ a[n], {n, 0, 4^9}]; Table[ b[[4^n + 1]], {n, 0, 9}]
%Y A078537 Cf. A002577, A078125, A078536.
%Y A078537 Column k=4 of A145515.
%K A078537 nonn
%O A078537 0,2
%A A078537 _Paul D. Hanna_, Nov 29 2002
%E A078537 Extended by _Robert G. Wilson v_, Dec 01 2002
%E A078537 More terms from _Alois P. Heinz_, Oct 11 2008