A105065 First entry of the vector v(n), where v(0) is the 2 by 2 column vector [0,1], v(n)=(M(n-1)^(n-1))v(n-1) and M(k) is the 2 x 2 matrix [[0,1],[1,k]].

0, 0, 1, 3, 79, 20135, 62508618, 2898048248280, 2373448827698520691, 39630346114940340723878803, 15291065219856512535000021521721585, 152375742915868882876218985340807522755957435

Offset

0,4

Links

Table of n, a(n) for n=0..11.

Example

We have v(1)=v(0), v(2)=M(1)v(1) is the column vector [1,1], v(3)=(M(2)^2)v(2) is the column vector [3,7]; consequently a(3)=3.

Maple

with(linalg): M:=n->matrix(2, 2, [0, 1, 1, n]): v[0]:=matrix(2, 1, [0, 1]): v[1]:=evalm(v[0]): for n from 2 to 11 do v[n]:=multiply(evalm(M(n-1)^(n-1)), v[n-1]) od: seq(v[n][1, 1], n=0..11);

Mathematica

M[0] = {{0, 1}, {1, 0}}; M[n_] := {{0, 1}, {1, n}} v[0] = {0, 1} v[n_] := v[n] = MatrixPower[M[n - 1], n - 1].v[n - 1] a = Table[v[n][[1]], {n, 0, 25}]

Crossrefs

Sequence in context: A331673 A065399 A265592 * A011187 A327250 A197248

Adjacent sequences: A105062 A105063 A105064 * A105066 A105067 A105068

Keyword

nonn

Author

Roger L. Bagula, Apr 05 2005

Extensions

Edited by N. J. A. Sloane, May 20 2006

Status

approved