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A022110
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Fibonacci sequence beginning 1, 20.
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4
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1, 20, 21, 41, 62, 103, 165, 268, 433, 701, 1134, 1835, 2969, 4804, 7773, 12577, 20350, 32927, 53277, 86204, 139481, 225685, 365166, 590851, 956017, 1546868, 2502885, 4049753, 6552638, 10602391, 17155029, 27757420, 44912449, 72669869, 117582318, 190252187
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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(20;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1) = 19. These are the SW-NE diagonals in P(20;n,k), the (20,1) 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) = 20.
G.f.: (1+19*x)/(1-x-x^2).
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MATHEMATICA
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a={}; b=1; c=20; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 12, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)
LinearRecurrence[{1, 1}, {1, 20}, 35] (* Paolo Xausa, Feb 22 2024 *)
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PROG
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(Magma) a0:=1; a1:=20; [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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