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A022104
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Fibonacci sequence beginning 1, 14.
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3
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1, 14, 15, 29, 44, 73, 117, 190, 307, 497, 804, 1301, 2105, 3406, 5511, 8917, 14428, 23345, 37773, 61118, 98891, 160009, 258900, 418909, 677809, 1096718, 1774527, 2871245, 4645772, 7517017, 12162789
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OFFSET
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0,2
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COMMENTS
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a(n-1)=sum(P(14;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=13. These are the SW-NE diagonals in P(14;n,k), the (14,1) Pascal triangle. Cf. A093645 for the (10,1) Pascal triangle. Observation by Paul Barry, Apr 29 2004. Proof via recursion relations and comparison of inputs.
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LINKS
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FORMULA
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a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=14. a(-1):=13.
G.f.: (1+13*x)/(1-x-x^2).
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MATHEMATICA
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a={}; b=1; c=14; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 9, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 22 2008 *)
LinearRecurrence[{1, 1}, {1, 14}, 40] (* Harvey P. Dale, Jun 12 2017 *)
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PROG
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(Magma) a0:=1; a1:=14; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..30]]; // Bruno Berselli, Feb 12 2013
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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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