A104100 First entry of the vector (M^n)v, where M is the 4 x 4 matrix [[0, 1, 3, 8], [0, 0, 1, 5], [0, 0, 0, 1], [1, 2, 1, 1]] and v is the column vector [[0, 1, 1, 2].

0, 20, 57, 434, 1717, 10553, 47573, 265684, 1276818, 6811097, 33775052, 176219759, 887333535, 4580070573, 23235380380, 119306276376, 607466542861, 3111219668378, 15869382126877, 81176527531045, 414414451168349

Offset

0,2

Comments

Characteristic polynomial of the matrix M is x^4-x^3-19x^2-10x-1.

Links

Table of n, a(n) for n=0..20.

Formula

Recurrence relation: a(n)=a(n-1)+19a(n-2)+10a(n-3)+a(n-4) for n>=4; a(0)=0, a(1)=20, a(2)=57, a(3)=434.

O.g.f.: x*(-20-37*x+3*x^2)/(-1+x+19*x^2+10*x^3+x^4). - R. J. Mathar, Dec 05 2007

Maple

a[0]:=0:a[1]:=20:a[2]:=57:a[3]:=434: for n from 4 to 22 do a[n]:=a[n-1]+19*a[n-2]+10*a[n-3]+a[n-4] od: seq(a[n], n=0..22);

Mathematica

Ms = {{0, 1, 3, 8}, {0, 0, 1, 5}, {0, 0, 0, 1}, {1, 2, 1, 1}}; z[0] = {0, 1, 1, 2}; z[n_] := z[n] = Ms.z[n - 1] a=Table[z[n][[1]], {n, 0, 50}]

Crossrefs

Sequence in context: A012483 A051872 A297397 * A069132 A124713 A126374

Adjacent sequences: A104097 A104098 A104099 * A104101 A104102 A104103

Keyword

nonn

Author

Roger L. Bagula, Mar 31 2005

Extensions

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

Status

approved