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A120656 6 X 6 trigonal prism bonding graph matrix Markov: this molecular structure is the major symmetry between the tetrahedron and cube: characteristic polynomial:12 x^2 - 4 x^3 - 9 x^4 + x^6. 0
0, 4, 18, 50, 166, 474, 1478, 4330, 13206, 39194, 118438, 353610, 1064246, 3185914, 9571398, 28686890, 86115286, 258236634, 774928358, 2324348170, 6973918326, 20920007354, 62763517318, 188283561450, 564864665366, 1694566034074 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (2, 5, -6).

FORMULA

Conjecture: a(n) = (-4+(-2)^n+2*3^(1+n))/3 for n>0. a(n) = 2*a(n-1)+5*a(n-2)-6*a(n-3) for n>3. G.f.: -2*x*(x-2)*(3*x+1)/((x-1)*(2*x+1)*(3*x-1)). [Colin Barker, Oct 19 2012]

MATHEMATICA

M = {{0, 1, 1, 1, 0, 0}, {1, 0, 1, 0, 1, 0}, {1, 1, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 1}, {0, 1, 0, 1, 0, 1}, {0, 0, 1, 1, 1, 0}} v[1] = {0, 1, 1, 2, 3, 5} v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]

Join[{0}, LinearRecurrence[{2, 5, -6}, {4, 18, 50}, 30]] (* Harvey P. Dale, Oct 18 2014 *)

CROSSREFS

Sequence in context: A181857 A303737 A180805 * A256431 A256430 A225263

Adjacent sequences:  A120653 A120654 A120655 * A120657 A120658 A120659

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Aug 10 2006

STATUS

approved

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)