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 A183895 Real part of a (-4,-4) Gaussian integer Somos-4 sequence. 4
 1, -1, -2, 8, 32, -128, -1024, 16384, 262144, -4194304, -134217728, 8589934592, 549755813888, -35184372088832, -4503599627370496, 1152921504606846976, 295147905179352825856, -75557863725914323419136, -38685626227668133590597632, 39614081257132168796771975168, 40564819207303340847894502572032, -41538374868278621028243970633760768, -85070591730234615865843651857942052864, 348449143727040986586495598010130648530944 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Real part of the Hankel transform of A183893(n)+I*A183894(n). A183895(n)+I*A183896(n) is a (-4,-4) Gaussian integer Somos-4 sequence. This is a generalized Somos-4 sequence. - Michael Somos, Mar 14 2020 LINKS G. C. Greubel, Table of n, a(n) for n = 0..114 FORMULA a(n) = (sqrt(1/4-sqrt(2)/8)*sin(7*Pi*n/4+3*Pi/8) +sqrt(sqrt(2)/8+1/4)*sin(5*Pi*n/4+Pi/8) +sqrt(sqrt(2)/8+1/4)*cos(3*Pi*n/4+3*Pi/8) + sqrt(1/4-sqrt(2)/8)*cos(Pi*n/4+Pi/8))*(-2)^floor(binomial(n+1,2)/2). From Michael Somos, Mar 14 2020: (Start) a(n) = (-1)^(n + floor(n/4)) * A160637(n). a(n) = a(-1-n) for all n in Z. 0 = a(n)*a(n+4) + 6*a(n+1)*a(n+3) + 4*a(n+2)^2 for all n in Z. 0 = a(n)*a(n+5) - 4*a(n+1)*a(n+4) for all n in Z. (End) MATHEMATICA Table[Round[(Sqrt[1/4 - Sqrt[2]/8]*Sin[7*Pi*n/4 + 3*Pi/8] + Sqrt[Sqrt[2]/8 + 1/4]*Sin[5*Pi*n/4 + Pi/8] + Sqrt[Sqrt[2]/8 + 1/4]*Cos[3*Pi*n/4 + 3*Pi/8] + Sqrt[1/4 - Sqrt[2]/8]*Cos[Pi*n/4 + Pi/8])*(-2)^(Floor[Binomial[n + 1, 2]/2])], {n, 0, 30}] (* G. C. Greubel, Feb 21 2018 *) a[ n_] := (-1)^(n + Quotient[n, 4])*(-2)^Quotient[n (n + 1), 4]; (* Michael Somos, Mar 14 2020 *) PROG (PARI) for(n=0, 30, print1(round((sqrt(1/4-sqrt(2)/8)*sin(7*Pi*n/4+3*Pi/8) +sqrt(sqrt(2)/8+1/4)*sin(5*Pi*n/4+Pi/8) +sqrt(sqrt(2)/8+1/4)*cos(3*Pi*n/4+3*Pi/8) + sqrt(1/4-sqrt(2)/8)*cos(Pi*n/4+Pi/8))*(-2)^floor( binomial( n+1, 2)/2)), ", ")) \\ G. C. Greubel, Feb 21 2018 (PARI) {a(n) = (-1)^(n + n\4) * (-2)^(n*(n+1)\4)}; /* Michael Somos, Mar 14 2020 */ (MAGMA) R:= RealField(); [Round((Sqrt(1/4-Sqrt(2)/8)*Sin(7*Pi(R)*n/4+3*Pi(R)/8) + Sqrt( Sqrt(2)/8+1/4)*Sin(5*Pi(R)*n/4+Pi(R)/8) +Sqrt(Sqrt(2)/8+1/4)*Cos(3* Pi(R)*n/4+3*Pi(R)/8) + Sqrt(1/4-Sqrt(2)/8)*Cos(Pi(R)*n/4+Pi(R)/8))*(-2)^Floor( Binomial( n+1, 2)/2)): n in [0..30]]; // G. C. Greubel, Feb 21 2018 CROSSREFS Cf. A160637. Sequence in context: A009117 A331407 A160637 * A228921 A150829 A155084 Adjacent sequences:  A183892 A183893 A183894 * A183896 A183897 A183898 KEYWORD sign AUTHOR Paul Barry, Jan 07 2011 STATUS approved

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Last modified October 23 23:52 EDT 2020. Contains 337975 sequences. (Running on oeis4.)