id:A088132 - OEIS Search Results

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a(n) equals the square of the n-th partial sum added to twice the n-th partial sum of the squares, divided by a(n-1), for all n>1, with a(0)=1, a(1)=3.

+0
2

1, 3, 12, 47, 185, 728, 2865, 11275, 44372, 174623, 687217, 2704496, 10643361, 41886227, 164840412, 648718287, 2552986921, 10047107272, 39539710801, 155605856283, 612376317860, 2409965560639, 9484256386273, 37324649227232 (list; graph; listen)

	OFFSET	`0,2`
	FORMULA	`a(n)=4a(n-1)-a(n-3) for n>3; G.f.: A(x)=(1-x)/(1-4x+x^3). 1 + xSum A088132(n)x^n = 1/(1 - xSum A030186(n)x^n).`
	PROGRAM	`(PARI) a(0)=1; a(1)=3; for(n=2, 30, a(n)=(sum(k=0, n-1, a(k))^2 + 2*sum(k=0, n-1, a(k)^2))/a(n-1))`
	CROSSREFS	`Cf. A088131, A030186.` `Adjacent sequences: A088129 A088130 A088131 this_sequence A088133 A088134 A088135` `Sequence in context: A047013 A108368 A077829 this_sequence A122450 A100389 A064562`
	KEYWORD	`nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Sep 19 2003`

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Last modified October 13 20:18 EDT 2008. Contains 145016 sequences.

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