A094569 Associated with alternating row sums of array in A094568.

2, 11, 78, 532, 3649, 25008, 171410, 1174859, 8052606, 55193380, 378301057, 2592914016, 17772097058, 121811765387, 834910260654, 5722560059188, 39223010153665, 268838511016464, 1842646566961586, 12629687457714635, 86565165637040862, 593326472001571396

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Clark Kimberling, Orderings of products of Fibonacci numbers, Fibonacci Quarterly, 42:1 (2004), pp. 28-35.

Index entries for linear recurrences with constant coefficients, signature (6,6,-1).

Formula

a(n) = F(4n+3) - a(n-1) for n >= 1, where a(0) = 2.

a(n) = (Fib(4n+5) + (-1)^n )/3. - Ralf Stephan, Dec 04 2004

a(n) = (-1)^n * sum((-1)^k*Fibonacci(4*k+3), k=0..n). - Gary Detlefs, Jan 22 2013

a(n) = 6*a(n-1) + 6*a(n-2) - a(n-3). - Colin Barker, Nov 19 2014

G.f.: -(x-2) / ((x+1)*(x^2-7*x+1)). - Colin Barker, Nov 19 2014

Example

Obtain 11,78,532 from a(0)=2 and Fibonacci numbers 13,89,610: 11=13-2, 78=89-11, 532=610-78.

Prog

(PARI) Vec(-(x-2)/((x+1)*(x^2-7*x+1)) + O(x^100)) \\ Colin Barker, Nov 19 2014
(PARI) vector(30, n, n--; (fibonacci(4*n+5) + (-1)^n)/3) \\ Michel Marcus, Nov 19 2014

Crossrefs

Cf. A000045, A094568, A094567.

Sequence in context: A120380 A369542 A079266 * A151418 A154273 A253256

Adjacent sequences: A094566 A094567 A094568 * A094570 A094571 A094572

Keyword

nonn,easy

Author

Clark Kimberling, May 12 2004

Extensions

More terms from Colin Barker, Nov 19 2014

Status

approved