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A122299
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Expansion of -x*(-1+x) / ( 1-2*x-3*x^2+x^3 ).
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0
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0, 1, 1, 5, 12, 38, 107, 316, 915, 2671, 7771, 22640, 65922, 191993, 559112, 1628281, 4741905, 13809541, 40216516, 117119750, 341079507, 993301748, 2892722267, 8424270271, 24533405595, 71446899736, 208069745986, 605946785585
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Lower right entry of the n-th power of the 5x5 matrix shown in the Mathematica program.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,3,-1)
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FORMULA
| a(n)= +2*a(n-1) +3*a(n-2) -a(n-3).
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MATHEMATICA
| M = {{1, 1, 1, 1, 1}, {1, 0, 0, 1, 0}, {1, 0, 1, 0, 0}, {1, 1, 0, 0, 0}, {1, 0, 0, 0, 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: A077918 A034752 A095310 * A162269 A028322 A169588
Adjacent sequences: A122296 A122297 A122298 * A122300 A122301 A122302
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KEYWORD
| nonn
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AUTHOR
| Gary Adamson and Roger Bagula (qntmpkt(AT)yahoo.com), Oct 19 2006
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