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A005363 Hoggatt sequence.
(Formerly M1867)
4
1, 2, 8, 44, 310, 2606, 25202, 272582, 3233738, 41454272, 567709144, 8230728508, 125413517530, 1996446632130, 33039704641922, 566087847780250, 10006446665899330, 181938461947322284, 3393890553702212368, 64807885247524512668, 1264344439859632559216 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..20.

D. C. Fielder, Letter to N. J. A. Sloane, Jun 1988

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 & C. O. Alford, An investigation of sequences derived from Hoggatt Sums and Hoggatt Triangles, Application of Fibonacci Numbers, 3 (1990) 77-88. Proceedings of 'The Third Annual Conference on Fibonacci Numbers and Their Applications,' Pisa, Italy, July 25-29, 1988. (Annotated scanned copy)

FORMULA

(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

a(n) = S(5,n) where S(d,n) is defined in A005364. - Sean A. Irvine, May 29 2016

MATHEMATICA

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 *)

CROSSREFS

Cf. A005364.

Sequence in context: A253950 A212913 A321628 * A216234 A123307 A293905

Adjacent sequences:  A005360 A005361 A005362 * A005364 A005365 A005366

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Simon Plouffe

EXTENSIONS

More terms from Sean A. Irvine, May 29 2016

STATUS

approved

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Last modified February 19 21:04 EST 2019. Contains 320328 sequences. (Running on oeis4.)