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 A078537 Number of partitions of 4^n into powers of 4 (without regard to order). 10
 1, 2, 6, 46, 1086, 79326, 18583582, 14481808030, 38559135542174, 357934565638890910, 11766678027350761752990, 1387043469046575118555443614, 592264246356176268834689653440926, 923812464024548700407122072128655860126, 5301247577915139769925461060755690116740047262 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Conjecture: a(n) = sum of the n-th row of lower triangular matrix A078536. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..60 FORMULA 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))...]. EXAMPLE 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]. MATHEMATICA 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}] CROSSREFS Cf. A002577, A078125, A078536. Column k=4 of A145515. Sequence in context: A316073 A001587 A306784 * A145502 A274702 A072444 Adjacent sequences:  A078534 A078535 A078536 * A078538 A078539 A078540 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 29 2002 EXTENSIONS Extended by Robert G. Wilson v, Dec 01 2002 More terms from Alois P. Heinz, Oct 11 2008 STATUS approved

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Last modified June 18 18:04 EDT 2021. Contains 345120 sequences. (Running on oeis4.)