A136408 a(n) = 3*a(n-1) - 4*a(n-2) + 6*a(n-3) - 4*a(n-4), with initial terms 1,2,4,7.

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

Author

Paul Curtz, Mar 31 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A077966.

Programs

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

Mathematica

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

PARI

a(n)=(5<Charles R Greathouse IV, Mar 30 2022

SageMath

[(5*2^n +2 -((n+1)%2)*(-2)^((n+1)//2))/6 for n in range(41)] # G. C. Greubel, Jan 19 2023

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)

Extensions

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