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A178376 A (-1,-2) Somos-4 sequence associated to the elliptic curve y^2 +y = x^3 +3*x^2 +x. 1
1, 1, -2, -3, -5, -28, 67, 411, -506, 10855, -74231, -664776, 7518457, -30009367, 1791756790, 22973709333, -762305126477, -10339529833556, -516074985082229, -26431010871217485, 1057255130388472846 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform of the sequence with g.f. 1/(1-x^2/(1+2x^2/(1+(3/4)x^2/(1-(10/9)x^2/(1-...,

where -2,-3/4,10/9,... are the x-coordinates of the multiples of (0,0).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..154

Paul Barry, Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials, arXiv:1910.00875 [math.CO], 2019.

FORMULA

a(n) = (-a(n-1)*a(n-3) - 2*a(n-2)^2)/a(n-4), n>3.

MATHEMATICA

RecurrenceTable[{a[n]==(-a[n-1]*a[n-3] -2*a[n-2]^2)/a[n-4], a[0] == 1, a[1] == 1, a[2] == -2, a[3] == -3}, a, {n, 0, 30}] (* G. C. Greubel, Sep 16 2018 *)

PROG

(PARI) m=30; v=concat([1, 1, -2, -3], vector(m-4)); for(n=5, m, v[n] = ( -v[n-1]*v[n-3] - 2*v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Sep 16 2018

(MAGMA) I:=[1, 1, -2, -3]; [n le 4 select I[n] else (-Self(n-1)*Self(n-3) - 2*Self(n-2)^2)/Self(n-4): n in [1..30]]; // G. C. Greubel, Sep 16 2018

CROSSREFS

Sequence in context: A247094 A078736 A042669 * A041585 A042935 A102926

Adjacent sequences:  A178373 A178374 A178375 * A178377 A178378 A178379

KEYWORD

easy,sign

AUTHOR

Paul Barry, May 26 2010

STATUS

approved

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Last modified May 29 08:07 EDT 2022. Contains 354122 sequences. (Running on oeis4.)