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 A058231 A Somos-8 sequence. 0
 0, 0, 1, 36, -16, 5041728, -19631351040, -62024429150208, -2805793044443561984, -1213280369793911777918976, 6452140445339288271043778576384, -30464666973776461531165746768673505280, 2509543205099684468628113981366827179048960, -83207632517142132982462515955707028888811707910062080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES D. G. Cantor (dgc(AT)ccrwest.org), email to N. J. A. Sloane, Nov. 30, 2000. LINKS D. G. Cantor, On the analogue of the division polynomials for hyperelliptic curves, J. Reine Angew. Math. (Crelle's J.) 447 (1994), pp. 91-145. R. W. Gosper and Richard C. Schroeppel, Somos Sequence Near-Addition Formulas and Modular Theta Functions, arXiv:math/0703470 [math.NT], 2007. FORMULA For all n, 0 = u[4] * a[n+4] * a[n-4] + u[3] * a[n+3] * a[n-3] + u[2] * a[n+2] * a[n-2] + u[1] * a[n+1] * a[n-1] + u[0] * a[n]^2, where u[0], ..., u[4] are 314101616640, 25442230947840, 235226865664, -181502208, -16. a(-n) = -a(n) for all n in Z. - Michael Somos, Jun 15 2011 MATHEMATICA (* Assuming the first 10 terms are known. *) init = {0, 0, 1, 36, -16, 5041728, -19631351040, -62024429150208, -2805793044443561984, -1213280369793911777918976}; init2 = Join[-Rest[init] // Reverse, init]; lg = Length[init]; rep = {u[0] -> 314101616640, u[1] -> 25442230947840, u[2] -> 235226865664, u[3] -> -181502208, u[4] -> -16}; Clear[a]; rec = u[4] a[n + 4] a[n - 4] + u[3] a[n + 3] a[n - 3] + u[2] a[n + 2] a[n - 2] + u[1] a[n + 1] a[n - 1] + u[0] a[n]^2 /. rep; (* Print[Solve[rec == 0, a[n+4]][[1]] /. n -> n-4]; *) a[n_] := a[n] = (1/a[n - 8])(16(1226959440 a[n - 4]^2 + 99383714640 a[n - 5] a[n - 3] + 918854944 a[n - 6] a[n - 2] - 708993 a[n - 7] a[n - 1])); Do[a[n] = init2[[n + lg]], {n, -(lg - 1), lg - 1}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Nov 08 2018 *) CROSSREFS Sequence in context: A260383 A056770 A061038 * A008894 A033973 A033356 Adjacent sequences:  A058228 A058229 A058230 * A058232 A058233 A058234 KEYWORD sign AUTHOR N. J. A. Sloane, Dec 02 2000 STATUS approved

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Last modified February 27 18:02 EST 2020. Contains 332307 sequences. (Running on oeis4.)