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A147543 Vertex counting using a vector matrix Markov with characteristic polynomial: 30 - 31 x + 10 x^2 - x^3. 0
6, 25, 105, 455, 2045, 9495, 45205, 219055, 1074045, 5305895, 26335205, 131090655, 653692045, 3263166295, 16299929205, 81451898255, 407116166045, 2035150690695, 10174462707205, 50868440641855, 254330583216045 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This pentagon vertex substitution result is a tessellation type form that has C5 rotational symmetry.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

Vertex substitutions on the pentagon: v2'=2*v2; v3'=3*v3; v5'=5*v5+5*v2; M = {{2, 0, 5}, {0, 3, 0}, {0, 0, 5}}; v(0) = {0, 5, 1}; v(n)=M.v(n-1); a(n)=Sum[v(n)[[m]],{m,1,3}].

a(n)= 10*a(n-1) -31*a(n-2) +30*a(n-3) = 5*3^n+8*5^n/3-5*2^n/3. G.f.: (6-35x+41*x^2)/((1-3x)(1-2x)(1-5x)). [From R. J. Mathar, Nov 09 2008]

MATHEMATICA

Clear[M, v, n, m, x]; M = {{2, 0, 5}, {0, 3, 0}, {0, 0, 5}}; v[0] = {0, 5, 1}; v[n_] := v[n] = M.v[n - 1]; Table[Sum[v[n][[m]], {m, 1, 3}], {n, 0, 20}]

CROSSREFS

Sequence in context: A267536 A029871 A188178 * A212258 A048875 A295202

Adjacent sequences:  A147540 A147541 A147542 * A147544 A147545 A147546

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Nov 06 2008

STATUS

approved

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Last modified September 27 16:11 EDT 2020. Contains 337383 sequences. (Running on oeis4.)