|
Search: id:A105065
|
|
|
| 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
1
|
|
| 0, 0, 1, 3, 79, 20135, 62508618, 2898048248280, 2373448827698520691, 39630346114940340723878803, 15291065219856512535000021521721585, 152375742915868882876218985340807522755957435
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
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: A073428 A062660 A065399 this_sequence A011187 A137994 A153709
Adjacent sequences: A105062 A105063 A105064 this_sequence A105066 A105067 A105068
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Roger Bagula (rlbagulatftn(AT)yahoo.com), Apr 05 2005
|
|
EXTENSIONS
|
Edited by N. J. A. Sloane (njas(AT)research.att.com), May 20 2006
|
|
|
Search completed in 0.002 seconds
|
