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A022130
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Fibonacci sequence beginning 4,9.
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9
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4, 9, 13, 22, 35, 57, 92, 149, 241, 390, 631, 1021, 1652, 2673, 4325, 6998, 11323, 18321, 29644, 47965, 77609, 125574, 203183, 328757, 531940, 860697, 1392637, 2253334, 3645971, 5899305, 9545276, 15444581, 24989857, 40434438, 65424295, 105858733, 171283028
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OFFSET
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0,1
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COMMENTS
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The associated Pisano series starts as in A001175, but differs for example for modulus 29 where it is 7, not 14. - R. J. Mathar, Nov 02 2011
The Pisano period also differs for modulus 58, where it is 21 instead of 42. Otherwise, the Pisano periods coincide with those of the Fibonacci numbers. - Klaus Purath, Jun 26 2022
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LINKS
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FORMULA
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a(n) = 4*Fibonacci(n+2) + Fibonacci(n).
a(n)= Fibonacci(n-2) + Fibonacci(n+5). - Gary Detlefs, Mar 31 2012
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MAPLE
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a:= n-> (<<0|1>, <1|1>>^n.<<4, 9>>)[1, 1]:
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MATHEMATICA
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a={}; b=4; c=9; 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 Joseph Stephan Orlovsky, Jul 23 2008 *)
LinearRecurrence[{1, 1}, {4, 9}, 40] (* Harvey P. Dale, Dec 15 2011 *)
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PROG
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(Magma) a0:=4; a1:=9; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..35]]; // Vincenzo Librandi, Jan 25 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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