A052956 a(n) = 2^n + Fibonacci(n+1).

2, 3, 6, 11, 21, 40, 77, 149, 290, 567, 1113, 2192, 4329, 8569, 16994, 33755, 67133, 133656, 266325, 531053, 1059522, 2114863, 4222961, 8434976, 16852241, 33675825, 67305282, 134535539, 268949685, 537702952, 1075088093, 2149661957

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1027

Index entries for linear recurrences with constant coefficients, signature (3,-1,-2).

Formula

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

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

a(n) = 2^n + Sum_{alpha=RootOf(-1+z+z^2)} (1 + 2*alpha)*alpha^(-1-n)/5.

Maple

spec:= [S, {S=Union(Sequence(Union(Prod(Z, Z), Z)), Sequence(Union(Z, Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
with(combinat); seq(2^n + fibonacci(n+1), n=0..40); # G. C. Greubel, Oct 22 2019

Mathematica

LinearRecurrence[{3, -1, -2}, {2, 3, 6}, 40] (* or *) Table[Fibonacci[n+1] + 2^n, {n, 0, 40}] (* G. C. Greubel, Oct 22 2019 *)

Prog

(PARI) vector(41, n, fibonacci(n) + 2^(n-1)) \\ G. C. Greubel, Oct 22 2019
(Magma) [2^n + Fibonacci(n+1): n in [0..40]]; // G. C. Greubel, Oct 22 2019
(Sage) [2^n + fibonacci(n+1) for n in (0..40)] # G. C. Greubel, Oct 22 2019
(GAP) List([0..40], n-> 2^n + Fibonacci(n+1) ); # G. C. Greubel, Oct 22 2019

Crossrefs

Cf. A000045, A000079.

Sequence in context: A371790 A306575 A006861 * A351972 A298118 A339292

Adjacent sequences: A052953 A052954 A052955 * A052957 A052958 A052959

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Extensions

More terms from James A. Sellers, Jun 05 2000

Status

approved