A078537 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(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