Search: id:A078537
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%I A078537
%S A078537 1,2,6,46,1086,79326,18583582,14481808030,38559135542174,
%T A078537 357934565638890910,11766678027350761752990,
%U A078537 1387043469046575118555443614,592264246356176268834689653440926
%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="b078537.txt">Table of n, a(n) for n = 0..20</
               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 Sequence in context: A052811 A078603 A001587 this_sequence A145502 A072444 
               A052596
%Y A078537 Adjacent sequences: A078534 A078535 A078536 this_sequence A078538 A078539 
               A078540
%K A078537 nonn
%O A078537 0,2
%A A078537 Paul D. Hanna (pauldhanna(AT)juno.com), Nov 29 2002
%E A078537 Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 01 2002
%E A078537 More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 11 2008

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