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A123007
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Scaled 2 X 2 vextor matrix Markov for characteristic Polynomial ( tin mean): -1 - 2 x/3 + x^2.
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0
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1, 3, 15, 57, 249, 1011, 4263, 17625, 73617, 305859, 1274271, 5301273, 22070985, 91853427, 382345719, 1591372281, 6623856033, 27570062595, 114754829487, 477640222329, 1988073910041, 8274909821043, 34442484832455
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.
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FORMULA
| M := {{0, 1}, {1, 2/3}}; v[1] = {1, 1}; v[n_] := v[n] = M.v[n - 1]; a(n) = v[n][[1]]
a(1)=1, a(2)=3, a(n)=2*a(n-1)+9*a(n-2) for n>2 . G.f.: x*(1+x)/(1-2x-9*x^2) - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2006
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MATHEMATICA
| M := {{0, 1}, {1, 2/3}}; v[1] = {1, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[v[n][[1]]*3^(n - 1), {n, 1, 30}]
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CROSSREFS
| Cf. A002534.
Sequence in context: A049161 A118048 A125673 * A121695 A017949 A049178
Adjacent sequences: A123004 A123005 A123006 * A123008 A123009 A123010
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 23 2006
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