A166516 - OEIS

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A166516

A product of consecutive doubled Fibonacci numbers.

1, 1, 2, 4, 10, 25, 65, 169, 442, 1156, 3026, 7921, 20737, 54289, 142130, 372100, 974170, 2550409, 6677057, 17480761, 45765226, 119814916, 313679522, 821223649, 2149991425, 5628750625, 14736260450, 38580030724, 101003831722 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	COMMENTS	`a(n+1)a(n+3)-a(n+2)^2=F(n+2)^2(1-(-1)^n)/2.`
	LINKS	`Index to sequences with linear recurrences with constant coefficients, signature (3,0,-3,1).`
	FORMULA	`G.f.: (-1+2x+x^2-x^3 ) / ( (x-1)(1+x)(x^2-3x+1) ).` `a(n)=F(2floor(n/2)+1)F(2floor((n-1)/2)+1)=F(A166514(2n))^2+F(A166514(2n+1))^2;` `a(n)=F(n)^2(1-(-1)^n)/2+F(n-1)*F(n+1)(1+(-1)^n)/2.`
	CROSSREFS	`Cf. A001654 (first differences).` `Sequence in context: A026269 A000645 A005958 * A189912 A195981 A124500` `Adjacent sequences: A166513 A166514 A166515 * A166517 A166518 A166519`
	KEYWORD	`easy,nonn`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Oct 16 2009`

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Last modified February 14 00:47 EST 2012. Contains 205567 sequences.