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

Author

Paul D. Hanna, Nov 29 2002

Keywords

• nonn

Comments

Conjecture: a(n) = sum of the n-th row of lower triangular matrix A078536.

Examples

			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].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..60

Crossrefs

Cf. A002577, A078125, A078536.

Column k=4 of A145515.

Programs

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}]

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))...].

Extensions

Extended by Robert G. Wilson v, Dec 01 2002

More terms from Alois P. Heinz, Oct 11 2008