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

1, 2, 6, 46, 1086, 79326, 18583582, 14481808030, 38559135542174, 357934565638890910, 11766678027350761752990, 1387043469046575118555443614, 592264246356176268834689653440926, 923812464024548700407122072128655860126, 5301247577915139769925461060755690116740047262

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