A136408 a(n) = 3*a(n-1) - 4*a(n-2) + 6*a(n-3) - 4*a(n-4).

1, 2, 4, 7, 13, 27, 55, 107, 211, 427, 859, 1707, 3403, 6827, 13675, 27307, 54571, 109227, 218539, 436907, 873643, 1747627, 3495595, 6990507, 13980331, 27962027, 55925419, 111848107, 223693483, 447392427, 894790315, 1789569707, 3579128491

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (3,-4,6,-4).

Formula

From R. J. Mathar, Apr 04 2008: (Start)

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

a(n) = (5*2^n + 2 - A077966(n))/6. (End)

Mathematica

LinearRecurrence[{3, -4, 6, -4}, {1, 2, 4, 7}, 41] (* Harvey P. Dale, Aug 12 2016 *)

Prog

(PARI) a(n)=(5<<n - imag(quadgen(-8)^(n+1)) + 2)/6 \\ Charles R Greathouse IV, Mar 30 2022
(Magma) [(5*2^n +2 -((n+1) mod 2)*(-2)^Floor((n+1)/2))/6: n in [0..40]]; // G. C. Greubel, Jan 19 2023
(SageMath) [(5*2^n +2 -((n+1)%2)*(-2)^((n+1)//2))/6 for n in range(41)] # G. C. Greubel, Jan 19 2023

Crossrefs

Cf. A077966.

Sequence in context: A112740 A309050 A265580 * A317718 A357931 A103104

Adjacent sequences: A136405 A136406 A136407 * A136409 A136410 A136411

Keyword

nonn,easy

Author

Paul Curtz, Mar 31 2008

Extensions

More terms from R. J. Mathar, Apr 04 2008

Status

approved