A098183 a(n) = 3*a(n-1) + a(n-3), a(0) = 1, a(1) = 1, a(2) = 4.

1, 1, 4, 13, 40, 124, 385, 1195, 3709, 11512, 35731, 110902, 344218, 1068385, 3316057, 10292389, 31945552, 99152713, 307750528, 955197136, 2964744121, 9201982891, 28561145809, 88648181548, 275146527535, 854000728414, 2650650366790, 8227097627905, 25535293612129

Offset: 0

Author

Paul Barry, Aug 30 2004

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,0,1).

Crossrefs

Cf. A098182, A098184.

Programs

Maple

a:= proc(n) option remember;
      `if`(n<2, 1, 3*a(n-1)+a(n-3))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, May 25 2022

Formula

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

a(n) = Sum_{k=0..floor(n/2)} binomial(n+k,3*k) * 3^k.