A078537 - OEIS

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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 (list; graph; refs; listen; history; 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..34`
	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 4 of A145515.` `Sequence in context: A052811 A078603 A001587 * A145502 A072444 A052596` `Adjacent sequences: A078534 A078535 A078536 * A078538 A078539 A078540`
	KEYWORD	`nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Nov 29 2002`
	EXTENSIONS	`Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 01 2002` `More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 11 2008`

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Last modified February 16 21:51 EST 2012. Contains 205978 sequences.