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A178418 A (-1, 2) Somos-4 sequence associated to the elliptic curve y^2 + 2*x*y + y = x^3 + x^2 + x. 1
1, 1, 2, 9, -1, 164, -737, 5895, -119558, -113489, -39697759, -800750664, -25602199327, -2344309254991, 14264330936074, -14182654502256615, 1282764246790221919, -163799892405003723284, 67851128001519788451263 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Hankel transform of the sequence with g.f. 1/(1-x^2/(1-2x^2/(1-(9/4)x^2/(1+(2/81)x^2/(1-1476x^2/(1-.... where 0/1, 2/1, 9/4, -2/81, 1476/1,... are the x-coordinates of the multiples of (0, 0).

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..125 (offset adapted by Georg Fischer, Jan 31 2019)

FORMULA

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

a(n) = -(-1)^n * a(-n), a(n+3)*a(n-2) = -a(n+2)*a(n-1) + 9*a(n+1)*a(n) for all n in Z. - Michael Somos, Sep 19 2018

EXAMPLE

G.f. = x + x^2 + 2*x^3 + 9*x^4 - x^5 + 164*x^6 - 737*x^7 + ... - Michael Somos, Sep 19 2018

MATHEMATICA

RecurrenceTable[{a[1]==a[2]==1, a[3]==2, a[4]==9, a[n]==(-a[n-1]a[n-3]+ 2a[n-2]^2)/a[n-4]}, a[n], {n, 20}] (* Harvey P. Dale, Sep 20 2011 *)

PROG

(PARI) m=30; v=concat([1, 1, 2, 9], 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 18 2018

(MAGMA) I:=[1, 1, 2, 9]; [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 18 2018

CROSSREFS

Sequence in context: A095178 A289632 A269919 * A249270 A153739 A298589

Adjacent sequences:  A178415 A178416 A178417 * A178419 A178420 A178421

KEYWORD

easy,sign

AUTHOR

Paul Barry, May 27 2010

EXTENSIONS

Offset changed to 1 by Michael Somos, Sep 19 2018

STATUS

approved

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Last modified December 4 15:01 EST 2020. Contains 338925 sequences. (Running on oeis4.)