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A058231
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A Somos-8 sequence.
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0
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0, 0, 1, 36, -16, 5041728, -19631351040, -62024429150208, -2805793044443561984, -1213280369793911777918976, 6452140445339288271043778576384, -30464666973776461531165746768673505280, 2509543205099684468628113981366827179048960, -83207632517142132982462515955707028888811707910062080
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OFFSET
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0,4
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REFERENCES
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D. G. Cantor (dgc(AT)ccrwest.org), email to N. J. A. Sloane, Nov. 30, 2000.
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LINKS
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FORMULA
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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.
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MATHEMATICA
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(* 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}];
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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