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A114725 The first entry of the vector v[n]=Mv[n-1], where M is the 6 X 6 matrix [[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 5, 10, 10, 5, 1]] and v[0] is the column vector [0, 1, 1, 2, 3, 5]. 1
0, 1, 1, 2, 3, 5, 55, 136, 502, 1799, 6247, 21902, 76882, 269498, 944895, 3313259, 11617291, 40733828, 142826195, 500794808, 1755948163, 6156922147, 21588159423, 75695064671, 265411365121, 930618039799 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Characteristic polynomial of the matrix M is x^6-(x+1)^5.

LINKS

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (1, 5, 10, 10, 5, 1).

FORMULA

Recurrence relation: a(n)=a(n-1)+5a(n-2)+10a(n-3)+10a(n-4)+5a(n-5)+a(n-6) for n>=6; a(0)=0,a(1)=a(2)=1,a(3)=2,a(4)=3,a(5)=5.

O.g.f.: x*(2*x+1)*(14*x^3+2*x-1)/(-1+x+5*x^2+10*x^3+10*x^4+5*x^5+x^6) . - R. J. Mathar, Dec 05 2007

MAPLE

a[0]:=0:a[1]:=1:a[2]:=1:a[3]:=2:a[4]:=3:a[5]:=5: for n from 6 to 25 do a[n]:=a[n-1]+5*a[n-2]+10*a[n-3]+10*a[n-4]+5*a[n-5]+a[n-6] od: seq(a[n], n=0..25);

MATHEMATICA

M = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 4, 6, 4, 1}}; w[0] = {0, 1, 1, 2, 3}; w[n_] := w[n] = M.w[n - 1] a = Flatten[Table[w[n][[1]], {n, 0, 25}]]

LinearRecurrence[{1, 5, 10, 10, 5, 1}, {0, 1, 1, 2, 3, 5}, 30] (* Harvey P. Dale, Jun 15 2014 *)

CROSSREFS

Sequence in context: A100850 A060085 A114370 * A136340 A029961 A083665

Adjacent sequences:  A114722 A114723 A114724 * A114726 A114727 A114728

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Feb 18 2006

EXTENSIONS

Edited by N. J. A. Sloane, May 13 2006

STATUS

approved

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Last modified June 17 21:47 EDT 2019. Contains 324200 sequences. (Running on oeis4.)