A104099 n * (10n^2 - 6n + 1), or n*A087348(n).

0, 5, 58, 219, 548, 1105, 1950, 3143, 4744, 6813, 9410, 12595, 16428, 20969, 26278, 32415, 39440, 47413, 56394, 66443, 77620, 89985, 103598, 118519, 134808, 152525, 171730, 192483, 214844, 238873, 264630, 292175, 321568, 352869, 386138, 421435

Offset

0,2

Comments

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

Characteristic polynomial of the matrix M is (x-1)^4.

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

Recurrence relation: a(n)=4a(n-1)-6a(n-2)+4a(n-3)-a(n-4) for n>=4; a(0)=0, a(1)=5, a(2)=58, a(3)=219.

O.g.f.: x*(5+38*x+17*x^2)/(-1+x)^4 = 132/(-1+x)^3+60/(-1+x)^4+89/(-1+x)^2+17/(-1+x) . - R. J. Mathar, Dec 05 2007

Maple

a[0]:=0:a[1]:=5:a[2]:=58:a[3]:=219: for n from 4 to 40 do a[n]:=4*a[n-1]-6*a[n-2]+4*a[n-3]-a[n-4] od: seq(a[n], n=0..40);

Mathematica

M = {{1, 2, 1, 1}, {0, 1, 3, 8}, {0, 0, 1, 5}, {0, 0, 0, 1}}; w[0] = {0, 1, 1, 2}; w[n_] := w[n] = M.w[n - 1] a=Table[w[n][[1]], {n, 0, 50}]
Table[n(10n^2-6n+1), {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 5, 58, 219}, 40] (* Harvey P. Dale, Sep 01 2018 *)

Prog

(PARI) a(n)=n*(10*n^2 - 6*n + 1) \\ Charles R Greathouse IV, Oct 18 2022

Crossrefs

Sequence in context: A295902 A290343 A173202 * A334698 A129897 A256218

Adjacent sequences: A104096 A104097 A104098 * A104100 A104101 A104102

Keyword

nonn,easy

Author

Roger L. Bagula, Mar 31 2005

Extensions

Edited by N. J. A. Sloane, May 20 2006, Jun 06 2007

Status

approved