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Search: id:A089074
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| A089074 |
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Let m0 be the matrix {{0,1,0,0},{0,0,1,0},{0,0,0,1},{1,1,1,1}}; a(n) = Floor[Re[MatrixPower[m0,n][[4,4]]]] |
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+0
1
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| 0, 1, 3, 7, 14, 28, 55, 107, 207, 400, 772, 1489, 2871, 5535, 10670, 20568, 39647, 76423, 147311, 283952, 547336, 1055025, 2033627, 3919943, 7555934, 14564532, 28074039, 54114451, 104308959, 201061984, 387559436, 747044833, 1439975215
(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*(1+x+x^2)/(1-2*x+x^5). a(n) = 2*a(n-1) - a(n-5) for n >= 6. - njas, Dec 05, 2003
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MATHEMATICA
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digits=100 NSolve[x^4-x^3-x^2-x-1==0, x] k=1.9275619754829254 q=k^2-k-1/k-1/k^2 m0={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 1, 1, q}} m[n_]=MatrixPower[m0, n] a=Table[Floor[Re[m[n][[4, 4]]]], {n, 1, digits}]
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CROSSREFS
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Equals A000078(n+3) + 1.
Adjacent sequences: A089071 A089072 A089073 this_sequence A089075 A089076 A089077
Sequence in context: A029879 A018084 A088209 this_sequence A125176 A125899 A052997
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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 04 2003
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