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A120663 Sequence produced by Markov chain based on 20 X 20 pentagonal prism bonding graph. 0
0, 67, 3079, 65458, 436705, 3325420, 21257887, 137628082, 852017725, 5260500568, 32028617995, 194422680046, 1174383558985, 7081178928436, 42616157629303, 256244634375850, 1539564650731285, 9246057306575824, 55510175964258211 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

3-d analog of D_5 dihedral and so(5) groups.

Characteristic polynomial = (-6 + x)(-4+ x)2(-2+ x)(-1 + x)4(1 + x)8(3 + x)4.

This represents an analog of the asymmetric field-like part of su(5) in 20 2 X 2 D5 matrices.

In the 1960's borohydrides were structurally used as analogs of nuclear internal structure models. In this case an so(5) is an analog of a pentagonal prism by way of the D5 dihedral symmetry involved. The hyper-analog doubling is the perpendicular so(5) like group. The secular determinant of these models is a way to approximate relative energy levels in higher dimensional spaces.

LINKS

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (9,-7,-93,152,84,-144).

FORMULA

G.f.: x*(129444*x^4-124633*x^3+38216*x^2+2476*x+67)/((x-1)*(x+1)*(2*x-1)*(3*x+1)*(4*x-1)*(6*x-1)). [Colin Barker, Nov 01 2012]

MATHEMATICA

M = {{0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0}} v[1] = Table[Fibonacci[n], {n, 0, 19}] v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}] a = Table[Floor[v[n][[1]]], {n, 1, 50}]

CROSSREFS

Sequence in context: A226713 A069397 A103727 * A261974 A078989 A156121

Adjacent sequences:  A120660 A120661 A120662 * A120664 A120665 A120666

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Aug 10 2006

EXTENSIONS

Edited by N. J. A. Sloane, Jul 13 2007

STATUS

approved

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Last modified November 12 07:16 EST 2019. Contains 329052 sequences. (Running on oeis4.)