A136298 a(n) = 3*a(n-1) - 4*a(n-3), with a(0)=1, a(1)=2, a(2)=4, a(3)=9.

1, 2, 4, 9, 19, 41, 87, 185, 391, 825, 1735, 3641, 7623, 15929, 33223, 69177, 143815, 298553, 618951, 1281593, 2650567, 5475897, 11301319, 23301689, 48001479, 98799161, 203190727, 417566265, 857502151, 1759743545, 3608965575

Offset: 0

Author

Paul Curtz, Mar 22 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 (3,0,-4).

Crossrefs

Cf. A001787, A078039.

Programs

Magma

[1] cat [(2^(n-2)*(31+3*n) - (-1)^n)/9: n in [1..40]]; // G. C. Greubel, Apr 12 2021

Mathematica

LinearRecurrence[{3,0,-4}, {1,2,4,9}, 41] (* G. C. Greubel, Apr 12 2021 *)

Sage

[1]+[(2^(n-2)*(31+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) = (7*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)*(3*n+31) - (-1)^n)/9 + (1/4)*[n=0].

E.g.f.: (1/36)*(9 - 4*exp(-x) + (31 + 6*x)*exp(2*x)). (End)

Extensions

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