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A120662 Sequence produced by 10 X 10 Markov chain based on 10 X 10 pentagonal prism bonding graph (3d analog of D5 dihedral and so(5) groups). 0
0, 12, 173, 861, 4979, 25545, 132419, 670689, 3390203, 17039337, 85505555, 428366577, 2144524907, 10730349369, 53675623811, 268448345025, 1342455212891, 6712910908041, 33566470310387, 167838076383633 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Characteristic polynomial: 240 x^4 + 352 x^5 + 120 x^6 - 40 x^7 - 25 x^8 + x^10.

In the 1960's borohydrides were structurally used as analogs to nuclear internal structure models. In this case an so(5) is an analog of a pendagonal prism by way of the D5 dihedral symmetry involved.

LINKS

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (6,1,-30).

FORMULA

a(n) = 6*a(n-1)+a(n-2)-30*a(n-3) for n>3. G.f.: -x*(189*x^2-101*x-12)/((2*x+1)*(3*x-1)*(5*x-1)). [Colin Barker, Nov 01 2012]

MATHEMATICA

M = {{0, 1, 1, 1, 1, 1, 0, 0, 0, 0}, {1, 0, 1, 1, 1, 0, 1, 0, 0, 0}, {1, 1, 0, 1, 1, 0, 0, 1, 0, 0}, {1, 1, 1, 0, 1, 0, 0, 0, 1, 0}, {1, 1, 1, 1, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 1, 1, 1, 1}, {0, 1, 0, 0, 0, 1, 0, 1, 1, 1}, {0, 0, 1, 0, 0, 1, 1, 0, 1, 1}, {0, 0, 0, 1, 0, 1, 1, 1, 0, 1}, {0, 0, 0, 0, 1, 1, 1, 1, 1, 0}} v[1] = Table[Fibonacci[n], {n, 0, 9}] v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]

LinearRecurrence[{6, 1, -30}, {0, 12, 173, 861}, 20] (* Harvey P. Dale, Jan 09 2019 *)

CROSSREFS

Sequence in context: A099270 A187361 A239335 * A230815 A099930 A307549

Adjacent sequences:  A120659 A120660 A120661 * A120663 A120664 A120665

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 July 10 15:20 EDT 2020. Contains 335576 sequences. (Running on oeis4.)