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A022133
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Fibonacci sequence beginning 4 15.
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1
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4, 15, 19, 34, 53, 87, 140, 227, 367, 594, 961, 1555, 2516, 4071, 6587, 10658, 17245, 27903, 45148, 73051, 118199, 191250, 309449, 500699, 810148, 1310847, 2120995, 3431842, 5552837, 8984679, 14537516
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| Tanya Khovanova, Recursive Sequences
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FORMULA
| Contribution from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 31 2008: (Start)
G.f.: (4+11*x)/(1-x-x^2).
a(n) = term (1,1) in the 1x2 matrix [4,11] . [1,1; 1,0]^n. (End)
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MAPLE
| (Maple) a := n -> (Matrix([[4, 11]]).Matrix([[1, 1], [1, 0]])^n)[1, 1]; seq (a(n), n=0..30); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 31 2008]
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MATHEMATICA
| a={}; b=4; c=15; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 40, 1}]; a (Vladimir Orlovsky, Jul 23 2008)
Alternate: Transpose[NestList[{#[[2]], #[[2]]+#[[1]]}&, {4, 15}, 40]][[1]]
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CROSSREFS
| Sequence in context: A032826 A190709 A166732 * A100783 A170850 A055465
Adjacent sequences: A022130 A022131 A022132 * A022134 A022135 A022136
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Alternate Mathematica program provided by Harvey P. Dale, Dec. 12, 2010
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