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A174168 A (1,3) Somos-4 sequence. 2
1, 2, 5, 17, 109, 706, 9529, 149057, 3464585, 141172802, 5987285341, 540281496721, 53055650250901, 8453268527614082, 2173247123169247025, 610193552206250342657, 364280506115937098013649, 225791960727416355391439746 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform of A128720.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..100

P. Barry, Generalized Catalan Numbers, Hankel Transforms and Somos-4 Sequences , J. Int. Seq. 13 (2010) #10.7.2.

P. Barry, Invariant number triangles, eigentriangles and Somos-4 sequences, arXiv preprint arXiv:1107.5490, 2011

FORMULA

a(n)=(a(n-1)*a(n-3)+3*a(n-2)^2)/a(n-4). - Index corrected, Franklin T. Adams-Watters, Oct 26 2011

MAPLE

A174168 := proc(n)

        if n <=4 then

                op(n+1, [1, 2, 5, 17, 109]) ;

        else

                (procname(n-1)*procname(n-3)+3*procname(n-2)^2)/procname(n-4) ;

        end if;

end proc: # R. J. Mathar, Oct 26 2011

MATHEMATICA

RecurrenceTable[{a[0]==1, a[1]==2, a[2]==5, a[3]==17, a[n]==(a[n-1]a[n-3]+ 3a[n-2]^2)/a[n-4]}, a[n], {n, 20}] (* Harvey P. Dale, Oct 25 2011 *)

PROG

(Haskell)

a174168 n = a174168_list !! n

a174168_list = [1, 2, 5, 17] ++ zipWith div (zipWith (+)

   (zipWith (*) (tail a174168_list) (drop 3 a174168_list))

                (map ((* 3) . (^ 2)) (drop 2 a174168_list))) a174168_list

-- Reinhard Zumkeller, Feb 13 2012

CROSSREFS

Sequence in context: A254132 A161609 A228238 * A097980 A210525 A074046

Adjacent sequences:  A174165 A174166 A174167 * A174169 A174170 A174171

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 10 2010

EXTENSIONS

More terms from Sean A. Irvine, Feb 12 2012

STATUS

approved

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Last modified November 21 05:01 EST 2017. Contains 294988 sequences.