A111573 a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4, with initial terms 0,1,3,3.

0, 1, 3, 3, 4, 8, 14, 21, 33, 55, 90, 144, 232, 377, 611, 987, 1596, 2584, 4182, 6765, 10945, 17711, 28658, 46368, 75024, 121393, 196419, 317811, 514228, 832040, 1346270, 2178309, 3524577, 5702887, 9227466, 14930352, 24157816, 39088169

Offset: 0

Author

Creighton Dement, Aug 10 2005

Keywords

• easy
• nonn

Comments

See comment and FAMP code for A111569.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,1,1).

Crossrefs

Cf. A001638, A111569, A111570, A111571, A111572, A111574, A111575, A111576.

Programs

Mathematica

Table[Fibonacci[n + 1] - Cos[n*Pi/2], {n, 0, 40}] (* Greg Dresden, Oct 16 2021 *)

Formula

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

a(n) = A056594(n+3) + A000045(n+1). - R. J. Mathar, Nov 10 2009

From Greg Dresden, Jan 15 2024: (Start)

a(2*n) = Fibonacci(n)*Lucas(n+1);

a(2*n+1) = Fibonacci(2*n+1). (End)

Extensions

Name clarified by Robert C. Lyons, Feb 06 2025