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A022393
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Fibonacci sequence beginning 1, 23.
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1
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1, 23, 24, 47, 71, 118, 189, 307, 496, 803, 1299, 2102, 3401, 5503, 8904, 14407, 23311, 37718, 61029, 98747, 159776, 258523, 418299, 676822, 1095121, 1771943, 2867064, 4639007, 7506071, 12145078, 19651149, 31796227, 51447376, 83243603, 134690979, 217934582, 352625561, 570560143
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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(23;n-1-k,k), n>=1, with a(-1)=22. These are the SW-NE diagonals in P(23;n,k), the (23,1) 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)=23. a(-1):=22.
G.f.: (1+22*x)/(1-x-x^2).
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MATHEMATICA
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LinearRecurrence[{1, 1}, {1, 23}, 30] (* Harvey P. Dale, Sep 30 2011 *)
Table[Fibonacci[n + 2] + 21*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) + 21*fibonacci(n), ", ")) \\ G. C. Greubel, Mar 02 2018
(Magma) [Fibonacci(n+2) + 21*Fibonacci(n): n in [0..50]]; // G. C. Greubel, Mar 02 2018
(GAP) List([0..40], n->Fibonacci(n+2)+21*Fibonacci(n)); # Muniru A Asiru, Mar 03 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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