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A005362 Hoggatt sequence.
(Formerly M1789)
3
1, 2, 7, 32, 177, 1122, 7898, 60398, 494078, 4274228, 38763298, 366039104, 3579512809, 36091415154, 373853631974, 3966563630394, 42997859838010, 475191259977060 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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.

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..17.

Nick Hobson, Python program for this sequence

FORMULA

(n+3)(n+4)(n+5)(n+6)a(n) = 6(n+1)(n+3)(n+4)(2n+5)a(n-1) + 4(n-1)n(4n+7)(4n+9)a(n-2); a(0)=1, a(1)=2 - Richard L. Ollerton (r.ollerton(AT)uws.edu.au), Sep 12 2006

a(n) = S(4,n) where S(d,n) is defined in A005364. - Sean A. Irvine, May 29 2016

MATHEMATICA

A005362[n_]:=HypergeometricPFQ[{-3-n, -2-n, -1-n, -n}, {2, 3, 4}, 1] (* Richard L. Ollerton (r.ollerton(AT)uws.edu.au), Sep 12 2006 *)

CROSSREFS

Cf. A005364.

Sequence in context: A143426 A125223 A277359 * A059439 A190123 A006014

Adjacent sequences:  A005359 A005360 A005361 * A005363 A005364 A005365

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Simon Plouffe

STATUS

approved

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Last modified April 30 13:46 EDT 2017. Contains 285669 sequences.