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A022391
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Fibonacci sequence beginning 1, 21.
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2
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1, 21, 22, 43, 65, 108, 173, 281, 454, 735, 1189, 1924, 3113, 5037, 8150, 13187, 21337, 34524, 55861, 90385, 146246, 236631, 382877, 619508, 1002385, 1621893, 2624278, 4246171, 6870449, 11116620, 17987069, 29103689, 47090758, 76194447, 123285205, 199479652, 322764857, 522244509
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OFFSET
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0,2
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COMMENTS
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a(n-1) = Sum_{k=0..ceiling((n-1)/2)} P(21;n-1-k,k), n>=1, with a(-1)=20. These are the SW-NE diagonals in P(21;n,k), the (21,1) 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)=21. a(-1):=20.
G.f.: (1+20*x)/(1-x-x^2).
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MATHEMATICA
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Table[Fibonacci[n + 2] + 19*Fibonacci[n], {n, 0, 50}] (* G. C. Greubel, Mar 02 2018 *)
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PROG
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(PARI) for(n=0, 50, print1(fibonacci(n+2) + 19*fibonacci(n), ", ")) \\ G. C. Greubel, Mar 02 2018
(Magma) [Fibonacci(n+2) + 19*Fibonacci(n): n in [0..50]]; // G. C. Greubel, Mar 02 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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