A166536 - OEIS

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A166536

A product of consecutive doubled Fibonacci numbers.

1, 3, 6, 16, 40, 105, 273, 715, 1870, 4896, 12816, 33553, 87841, 229971, 602070, 1576240, 4126648, 10803705, 28284465, 74049691, 193864606, 507544128, 1328767776, 3478759201, 9107509825, 23843770275, 62423800998, 163427632720 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,2`
	COMMENTS	`a(n)a(n+2)-a(n+1)^2=(-1)^n(F(2n+4)-1).`
	LINKS	`Index to sequences with linear recurrences with constant coefficients, signature (3,0,-3,1)`
	FORMULA	`G.f.: (1-3x^2+x^3)/(1-3x+3x^3-x^4).` `a(n)=F(n+1)F(n+2)+(1-(-1)^n)/2;` `a(n)=(F(n+2)(1+(-1)^n)/2+F(n)(1-(-1)^n)/2)(F(n+3)(1-(-1)^n)/2+F(n+1)*(1+(-1)^n)/2).`
	CROSSREFS	`Cf. A166516.` `Sequence in context: A046211 A205770 A018022 * A128720 A096745 A027088` `Adjacent sequences: A166533 A166534 A166535 * A166537 A166538 A166539`
	KEYWORD	`easy,nonn`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Oct 16 2009`

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Last modified February 17 10:05 EST 2012. Contains 206009 sequences.