A271358 a(n) = k*Fibonacci(2*n+1) + (k+1)*Fibonacci(2*n), where k=4.

4, 13, 35, 92, 241, 631, 1652, 4325, 11323, 29644, 77609, 203183, 531940, 1392637, 3645971, 9545276, 24989857, 65424295, 171283028, 448424789, 1173991339, 3073549228, 8046656345, 21066419807, 55152603076, 144391389421, 378021565187, 989673306140

Offset

0,1

Links

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

Boothby, T.; Burkert, J.; Eichwald, M.; Ernst, D. C.; Green, R. M.; Macauley, M.  On the cyclically fully commutative elements of Coxeter groups, J. Algebr. Comb. 36, No. 1, 123-148 (2012) Table 1 CFC Type D.

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

Formula

G.f.: (4+x) / (1-3*x+x^2).

a(n) = 3*a(n-1)-a(n-2) for n>1.

a(n) = (2^(-2-n)*((11-sqrt(5))*(3+sqrt(5))^(n+1) - (11+sqrt(5))*(3-sqrt(5))^(n+1))) / sqrt(5).

a(n) = 5*Fibonacci(2*n+2) - Fibonacci(2*n+1).

a(n) = 4*A001906(n+1) + A001906(n-1).

Prog

(PARI) a(n) = 4*fibonacci(2*n+1) + 5*fibonacci(2*n)
(PARI) Vec((4+x)/(1-3*x+x^2) + O(x^50))
(Magma) k:=4; [k*Fibonacci(2*n+1)+(k+1)*Fibonacci(2*n): n in [0..30]]; // Bruno Berselli, Apr 06 2016

Crossrefs

Cf. A000045.

Cf. A001906 (k=0), A002878 (k=1), A100545 (k=2, without the initial 2), A271357 (k=3), this sequence (k=4), A271359 (k=5).

Sequence in context: A189595 A189602 A317781 * A306349 A268996 A270988

Adjacent sequences: A271355 A271356 A271357 * A271359 A271360 A271361

Keyword

nonn,easy

Author

Colin Barker, Apr 05 2016

Extensions

Changed offset and adapted definition, programs and formulas by Bruno Berselli, Apr 06 2016

Status

approved