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A166516 A product of consecutive doubled Fibonacci numbers. 6
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; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (3,0,-3,1).

FORMULA

G.f.: (-1+2*x+x^2-x^3 ) / ( (x-1)*(1+x)*(x^2-3*x+1) ).

a(n) = F(2*floor(n/2)+1)*F(2*floor((n-1)/2)+1).

a(n) = 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.

a(n+1)*a(n+3) - a(n+2)^2 = F(n+2)^2*(1-(-1)^n)/2.

a(n) = 3*a(n-1) - 3*a(n-3) + a(n-4). - G. C. Greubel, May 15 2016

MATHEMATICA

CoefficientList[Series[(-1+2x+x^2-x^3)/((x-1)(1+x)(x^2-3x+1)), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, 0, -3, 1}, {1, 1, 2, 4}, 30] (* Harvey P. Dale, Dec 26 2013 *)

CROSSREFS

Cf. A001654 (first differences).

Sequence in context: A026269 A000645 A005958 * A230552 A230555 A189912

Adjacent sequences:  A166513 A166514 A166515 * A166517 A166518 A166519

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 16 2009

STATUS

approved

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Last modified February 19 22:36 EST 2020. Contains 332061 sequences. (Running on oeis4.)