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A174013 Sequence whose Hankel transform is a (1,1) Somos-4 sequence. 2
1, 1, 3, 6, 12, 22, 37, 56, 73, 75, 44, -21, -39, 297, 1751, 5749, 14104, 27136, 38163, 22135, -80421, -369611, -934754, -1637758, -1559395, 2019629, 14766699, 44732254, 94865112, 138114302, 61077521 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Continued fraction form of g.f. A(x) given by A(x)=1/(1-x(1+x)/(1-x/(1+x*A(x))).

Hankel transform is A174017. Diagonal sums of the Deleham array

[1,1,-1,1,1,-1,1,...] Delta [1,0,0,1,0,0,1,0,0,1,0,...], or A174014.

LINKS

Table of n, a(n) for n=0..30.

FORMULA

G.f.: (1-3x-x^2-sqrt(1-2x-x^2+6x^3+5x^4))/(2x(1-x-x^2));

G.f.: 1/(1-x(1+x)/(1-x/(1+x/(1-x(1+x)/(1-x/(1+x/(1-... continued fraction).

Conjecture: (n+1)*a(n) +n*a(n-1) +12*(-n+1)*a(n-2) +3*(3*n-8)*a(n-3) +6*(6*n-23)*a(n-4) +11*(-n+2)*a(n-5) +(-49*n+253)*a(n-6) +20*(-n+6)*a(n-7)=0. - R. J. Mathar, Jan 12 2013

CROSSREFS

Sequence in context: A280473 A139422 A062483 * A081056 A242448 A066982

Adjacent sequences:  A174010 A174011 A174012 * A174014 A174015 A174016

KEYWORD

easy,sign

AUTHOR

Paul Barry, Mar 05 2010

STATUS

approved

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Last modified July 16 04:26 EDT 2019. Contains 325064 sequences. (Running on oeis4.)