A109522 a(n) = the (1,2)-entry in the matrix P^n + F^n, where the 2 X 2 matrices P and F are defined by P=[0,1;1,0] and F=[0,1;1,1].

0, 2, 1, 3, 3, 6, 8, 14, 21, 35, 55, 90, 144, 234, 377, 611, 987, 1598, 2584, 4182, 6765, 10947, 17711, 28658, 46368, 75026, 121393, 196419, 317811, 514230, 832040, 1346270, 2178309, 3524579, 5702887, 9227466, 14930352, 24157818, 39088169

Offset

0,2

Links

Table of n, a(n) for n=0..38.

Formula

a(n) = A052959(n-1). - R. J. Mathar, Aug 18 2008

Example

a(8)=21 because P^8=[1,0;0,1], F^8=[13,21;21,34] and so P^8+F^8=[14,21;21,34].

Maple

with(linalg): a:=proc(n) local P, F, v, k: P[1]:=matrix(2, 2, [0, 1, 1, 0]): F[1]:=matrix(2, 2, [0, 1, 1, 1]): v:=matrix(2, 1, [0, 1]): for k from 2 to n do P[k]:=multiply(P[1], P[k-1]): F[k]:=multiply(F[1], F[k-1]) od: evalm(P[n]+F[n])[1, 2] end: 0, seq(a(n), n=1..44);

Mathematica

v[0] = {0, 1}; w[0] = {0, 1}; M2 = {{0, 1}, {1, 0}}; Mf = {{0, 1}, {1, 1}} v[n_] := v[n] = M2.v[n - 1] w[n_] := w[n] = Mf.w[n - 1] a = Table[(w[n] + v[n])[[1]], {n, 0, 50}]

Crossrefs

Cf. A000045.

Sequence in context: A241379 A108949 A167704 * A052959 A346473 A257702

Adjacent sequences: A109519 A109520 A109521 * A109523 A109524 A109525

Keyword

nonn

Author

Roger L. Bagula, Jun 17 2005

Status

approved