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 A073999 Number of strings of length n over GF(4) with trace 1 and subtrace x where x = RootOf(z^2+z+1). 10
 0, 0, 3, 16, 60, 240, 1008, 4096, 16320, 65280, 261888, 1048576, 4193280, 16773120, 67104768, 268435456, 1073725440, 4294901760, 17179803648, 68719476736, 274877644800, 1099510579200, 4398045462528, 17592186044416, 70368739983360, 281474959933440, 1125899890065408, 4503599627370496, 18014398442373120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Same as the number of strings of length n over GF(4) with trace x and subtrace 1. Same as the number of strings of length n over GF(4) with trace y and subtrace 1 where y = 1+x. Same as the number of strings of length n over GF(4) with trace 1 and subtrace y. Same as the number of strings of length n over GF(4) with trace x and subtrace x. Same as the number of strings of length n over GF(4) with trace y and subtrace y. LINKS Table of n, a(n) for n=1..29. F. Ruskey, Strings over GF(4) with given trace and subtrace Index entries for linear recurrences with constant coefficients, signature (6,-12,24,-32). FORMULA a(n; t, s) = a(n-1; t, s) + a(n-1; t-1, s-(t-1)) + a(n-1; t-2, s-2(t-2)) + a(n-1; t-3, s-3(t-3)) where t is the trace and s is the subtrace. Note that all operations involving operands t or s are carried out over GF(4). G.f.: -(2*q-3)*q^3/[(1-2q)(1-4q)(1+4q^2)]. - Lawrence Sze, Oct 24 2004 a(n) = -2^(n-3) +( (-2i)^n + (2i)^n +4^n )/16 with i=sqrt(-1). - R. J. Mathar, Nov 18 2011 MATHEMATICA LinearRecurrence[{6, -12, 24, -32}, {0, 0, 3, 16}, 30] (* Harvey P. Dale, Mar 12 2019 *) CROSSREFS Cf. A073995, A073996, A073997, A073998. Sequence in context: A005550 A210323 A062474 * A259056 A155160 A370305 Adjacent sequences: A073996 A073997 A073998 * A074000 A074001 A074002 KEYWORD easy,nonn AUTHOR Frank Ruskey and Nate Kube, Aug 16 2002 EXTENSIONS More terms from Max Alekseyev, Apr 16 2013 STATUS approved

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Last modified June 13 15:37 EDT 2024. Contains 373389 sequences. (Running on oeis4.)