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A123959
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Let M be the 5 X 5 matrix {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {-8, -8, 8, 4, 0}}; let v[1] = {0, 0, 0, 0, 1}'; v[n] = M.v[n - 1]'; then a(n) = v[n]'[[1]] (the prime denotes transposition).
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0, 0, 0, 0, 1, 0, 4, 8, 8, 56, 64, 192, 576, 768, 2880, 5632, 11520, 34816, 61952, 163328, 389120, 778240, 2088960, 4423680, 10162176, 25067520, 53100544, 129466368, 296255488, 660832256, 1595408384, 3552837632, 8262516736
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| A 5 X 5 vector matrix Markov chain based on a shifted Chebyshev recursive characteristic polynomial: -8 - 8 x + 8 x^2 + 4 x^3 - x^5 <- (-1 + 4 y + 8 y^2 - 8 y^3 - 8 y^4).
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MATHEMATICA
| M = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {-8, -8, 8, 4, 0}}; v[1] = {0, 0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
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CROSSREFS
| Sequence in context: A195752 A095806 A096872 * A096412 A153109 A198736
Adjacent sequences: A123956 A123957 A123958 * A123960 A123961 A123962
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KEYWORD
| nonn
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AUTHOR
| Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Oct 27 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Mar 30 2007
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