A136299 a(n) = 3*a(n-1) - 4*a(n-3), with a(0)=1, a(1)=2, a(2)=4, a(3)=7.

1, 2, 4, 7, 13, 23, 41, 71, 121, 199, 313, 455, 569, 455, -455, -3641, -12743, -36409, -94663, -233017, -553415, -1281593, -2912711, -6524473, -14447047, -31690297, -68972999, -149130809, -320631239, -686001721, -1461481927, -3101920825, -6561755591, -13839339065

Offset: 0

Author

Paul Curtz, Mar 22 2008

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,0,-4).

Crossrefs

Cf. A001787, A051013.

Programs

Magma

[1] cat [(2^(n-2)*(41-3*n) + (-1)^n)/9: n in [1..40]]; // G. C. Greubel, Apr 12 2021

Mathematica

LinearRecurrence[{3,0,-4}, {1,2,4,7}, 41] (* G. C. Greubel, Apr 12 2021 *)

Sage

[1]+[(2^(n-2)*(41-3*n) + (-1)^n)/9 for n in (1..40)] # G. C. Greubel, Apr 12 2021

Formula

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

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

a(n) = (11*2^n + (-1)^n)/9 - A001787(n+1)/12 if n>0. (End)

From G. C. Greubel, Apr 12 2021: (Start)

a(n) = (2^(n-2)*(41-3*n) + (-1)^n)/9 - (1/4)*[n=0].

E.g.f.: (-9 + 4*exp(-x) + (41 - 6*x)*exp(2*x))/36. (End)