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Search: id:A089068
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| A089068 |
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Let m0 be the 3 X 3 matrix {{0,1,0},{0,0,1},{1,1,q}}; then a(n) = (3,3)-element of m0^n. |
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4
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| 0, 1, 3, 6, 12, 23, 43, 80, 148, 273, 503, 926, 1704, 3135, 5767, 10608, 19512, 35889, 66011, 121414, 223316, 410743, 755475, 1389536, 2555756, 4700769, 8646063, 15902590, 29249424, 53798079, 98950095, 181997600, 334745776, 615693473
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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G.f.: [x^2(1+x)]/[(1-x)(1-x-x^2-x^3)].
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MATHEMATICA
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digits=100 NSolve[x^3-x^2-x-1==0, x] k=1.83928675521416113 q=k^2-k-1/k m0={{0, 1, 0}, {0, 0, 1}, {1, 1, q}} m[n_]=MatrixPower[m0, n] a=Table[Floor[Re[m[n][[3, 3]]]], {n, 1, digits}]
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CROSSREFS
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Pairwise sums of A008937, A018921.
Cf. A027114.
Adjacent sequences: A089065 A089066 A089067 this_sequence A089069 A089070 A089071
Sequence in context: A097939 A162506 A055244 this_sequence A018180 A079735 A050243
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 03 2003
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