A151889 a(1)=2, a(2)=3; a(2k-1)=2a(2k-2)+a(2k-3), a(2k)=3a(2k-2)+2a(2k-3), k >= 2.

2, 3, 8, 13, 34, 55, 144, 233, 610, 987, 2584, 4181, 10946, 17711, 46368, 75025, 196418, 317811, 832040, 1346269, 3524578, 5702887, 14930352, 24157817, 63245986, 102334155, 267914296, 433494437, 1134903170, 1836311903

Offset: 1

Author

Antonia Redondo Buitrago (aredondo(AT)sabuco.com), Jul 23 2009

Keywords

• nonn
• easy

Comments

Because of G.f. in Formula section, numbers k + 1 such that A054347(k)/k is an integer. - Ctibor O. Zizka, Apr 02 2025

Links

• Index entries for linear recurrences with constant coefficients, signature (0,4,0,1).

Crossrefs

Cf. A000045, A000201, A054347.

Programs

Mathematica

LinearRecurrence[{0,4,0,1},{2,3,8,13},30] (* Harvey P. Dale, Dec 31 2021 *)

PARI

a(n) = if (n==1, 2, if (n==2, 3, if (n%2, 2*a(n-1)+a(n-2), 3*a(n-2)+2*a(n-3)))) \\ Michel Marcus, Jun 20 2013

Formula

a(2k-1) = Fib(3k-1), a(2k) = Fib(3k).

G.f.: -(x^3+3*x+2)*x/(x^4+4*x^2-1). - Alois P. Heinz, Jun 20 2013