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A096084 Allometric version of a first tridiagonal sequence. 1
13, 950, 95988, 10905817, 1286148527, 153328417883, 18334828728774, 2194320791239995, 262679450252979836, 31447103467743125966, 3764810710887551357911, 450721059410647384921011 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This seems to be just the expansion of ( -x*(13-1065*x+4508*x^2+74*x^3) ) / ( (2*x-1)*(37*x^3+3984*x^2-153*x+1) ) with a(n) = +155*a(n-1) -4290*a(n-2) +7931*a(n-3) +74*a(n-4). - R. J. Mathar, Oct 30 2011

LINKS

Table of n, a(n) for n=1..12.

FORMULA

A=4 X 4 tridiagonal matrix a(n, 1) =(3*A^3-a^2)^n*{1, 1, 1, 1}

MATHEMATICA

N0=4 v=Table[1, {n, 1, N0}] a0=2*IdentityMatrix[N0] a0[[N0, N0]]=1 a1=Table[If[n-m+1==0, -1, 0], {n, 1, N0}, {m, 1, N0}] a2=Table[If[m-n+1==0, -1, 0], {n, 1, N0}, {m, 1, N0}] a=a0+a1+a2 (* allometric matrix N-K>exp{1]*) anm=3*MatrixPower[a, 3]-MatrixPower[a, 2] digits=25 aa=Table[MatrixPower[anm, n].v, {n, 1, digits}] aa1=Table[aa[[n, 1]], {n, 1, digits}] anm=3*MatrixPower[a, 3]-MatrixPower[a, 2]

CROSSREFS

Sequence in context: A197068 A274544 A267915 * A203708 A301870 A297739

Adjacent sequences:  A096081 A096082 A096083 * A096085 A096086 A096087

KEYWORD

nonn,uned,obsc

AUTHOR

Roger L. Bagula, Jul 21 2004

EXTENSIONS

Warning: This entry has not been edited and may contain errors. It is included on a provisional basis in the hope that some reader will edit it. - N. J. A. Sloane.

STATUS

approved

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Last modified August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)