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 A178417 A (-1,1) Somos-4 sequence associated to the elliptic curve y^2 + x*y + y = x^3 + x^2 + x. 1
 1, 1, 1, 4, -3, 19, -67, 40, -1243, -4299, -25627, -334324, 627929, -29742841, 372632409, -1946165680, 128948361769, 1488182579081, 52394610324649, 2333568937567764, -5642424912729707, 3857844273728205019 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Hankel transform of the sequence with g.f. 1/(1-x^2/(1-x^2/(1-4x^2/(1+(3/16)x^2/(1-(76/9)x^2/(1-.... where 1,4,-3/16,76/9,... are the x-coordinates of the multiples of (0,0). LINKS G. C. Greubel, Table of n, a(n) for n = 1..156 (offset adapted by Georg Fischer, Jan 31 2019). FORMULA a(n) = (-a(n-1)*a(n-3) + a(n-2)^2)/a(n-4), n>3. a(n) = -(-1)^n*a(-n) for all n in Z. - Michael Somos, Sep 17 2018 EXAMPLE G.f. = x + x^2 + x^3 + 4*x^4 - 3*x^5 + 19*x^6 - 67*x^7 + ... - Michael Somos, Sep 17 2018 MATHEMATICA RecurrenceTable[{a[n] == (-a[n-1]*a[n-3] +a[n-2]^2)/a[n-4], a[0] == 1, a[1] == 1, a[2] == 1, a[3] == 4}, a, {n, 0, 30}] (* G. C. Greubel, Sep 16 2018 *) PROG (PARI) m=30; v=concat([1, 1, 1, 4], vector(m-4)); for(n=5, m, v[n] = ( -v[n-1]*v[n-3] +v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Sep 16 2018 (MAGMA) I:=[1, 1, 1, 4]; [n le 4 select I[n] else (-Self(n-1)*Self(n-3) + Self(n-2)^2)/Self(n-4): n in [1..30]]; // G. C. Greubel, Sep 16 2018 CROSSREFS Sequence in context: A192773 A183231 A241358 * A178628 A167479 A278424 Adjacent sequences:  A178414 A178415 A178416 * A178418 A178419 A178420 KEYWORD easy,sign AUTHOR Paul Barry, May 27 2010 EXTENSIONS Changed offset to 1 by Michael Somos, Sep 17 2018 STATUS approved

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Last modified October 30 05:44 EDT 2020. Contains 338077 sequences. (Running on oeis4.)