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Search: id:A005363
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| A005363 |
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Hoggatt sequence.
(Formerly M1867)
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+0
4
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| 1, 2, 8, 44, 310, 2606, 25202, 272582, 3233738, 41454272, 567709144, 8230728508, 125413517530, 1996446632130, 33039704641922, 566087847780250, 10006446665899330
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. C. Fielder and C. O. Alford, On a conjecture by Hoggatt with extensions to Hoggatt sums and Hoggatt triangles, Fib. Quart., 27 (1989), 160-168.
D. C. Fielder and C. O. Alford, ``An investigation of sequences derived from Hoggatt sums and Hoggatt triangles,'' in G. E. Bergum et al., editors, Applications of Fibonacci Numbers: Proc. Third Internat. Conf. on Fibonacci Numbers and Their Applications, Pisa, Jul 25-29, 1988. Kluwer, Dordrecht, Vol. 3, 1990, pp. 77-88.
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FORMULA
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(n+4)(n+5)^2(n+6)(n+7)(n+8)(252+253n+55n^2)a(n) = 3(n+4)(n+5)(141120+362152n+373054n^2+192647n^3+52441n^4+7161n^5+385n^6)a(n-1) + n(n-1)(5738880+14311976n+14466242n^2+7579175n^3+2170343n^4+322289n^5+19415n^6)a(n-2) - 32(n-1)^2 n^2(n-2)(n+1)(560 + 363n + 55n^2)a(n-3); a(-1)=a(0)=1, a(1)=2 - Richard L. Ollerton (r.ollerton(AT)uws.edu.au), Sep 12 2006
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MATHEMATICA
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A005363[n_]:=HypergeometricPFQ[{-4-n, -3-n, -2-n, -1-n, -n}, {2, 3, 4, 5}, -1] - Richard L. Ollerton (r.ollerton(AT)uws.edu.au), Sep 12 2006
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CROSSREFS
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Sequence in context: A052897 A137984 A005649 this_sequence A123307 A126101 A157994
Adjacent sequences: A005360 A005361 A005362 this_sequence A005364 A005365 A005366
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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