A183893
Real part of a Gaussian integer sequence with a Gaussian integer Somos-4 Hankel transform.
Original entry on oeis.org
1, 1, -1, -1, 9, 9, -73, -73, 697, 697, -7161, -7161, 77457, 77457, -868881, -868881, 10016241, 10016241, -117935473, -117935473, 1412307481, 1412307481, -17148100569, -17148100569, 210619695913, 210619695913, -2612194773481, -2612194773481, 32668519882017, 32668519882017, -411515480555553
Offset: 0
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[Round(Real((&+[(Sqrt(-1))^k*Binomial(2*k,k)*Binomial( Floor((n+k)/2),k)/(k+1): k in [0..n]]))): n in [0..30]]; // G. C. Greubel, Feb 21 2018
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Table[Re[Sum[I^k*Binomial[2*k, k]*Binomial[Floor[(n + k)/2], k]/(k + 1), {k, 0, n}]], {n, 0, 50}] (* G. C. Greubel, Feb 21 2018 *)
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for(n=0,50, print1(real(sum(k=0,n, I^k*binomial(2*k,k)* binomial( floor((n+k)/2),k)/(k+1) )), ", ")) \\ G. C. Greubel, Feb 21 2018
A183894
Imaginary part of a Gaussian integer sequence with a Gaussian integer Somos-4 Hankel transform.
Original entry on oeis.org
0, 1, 1, -3, -3, 25, 25, -223, -223, 2217, 2217, -23427, -23427, 258417, 258417, -2941311, -2941311, 34289041, 34289041, -407344771, -407344771, 4913508489, 4913508489, -60018592735, -60018592735, 740910077497, 740910077497, -9228860168451, -9228860168451, 115849095339489, 115849095339489
Offset: 0
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[Round(Imaginary((&+[(Sqrt(-1))^k*Binomial(2*k,k)*Binomial( Floor((n+k)/2),k)/(k+1): k in [0..n]]))): n in [0..30]]; // G. C. Greubel, Feb 21 2018
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Table[Im[Sum[I^k*Binomial[2*k, k]*Binomial[Floor[(n + k)/2], k]/(k + 1), {k, 0, n}]], {n, 0, 50}] (* G. C. Greubel, Feb 21 2018 *)
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for(n=0,50, print1(imag(sum(k=0,n, I^k*binomial(2*k,k)* binomial( floor((n+k)/2),k)/(k+1) )), ", ")) \\ G. C. Greubel, Feb 21 2018
A183895
Real part of a (-4,-4) Gaussian integer Somos-4 sequence.
Original entry on oeis.org
1, -1, -2, 8, 32, -128, -1024, 16384, 262144, -4194304, -134217728, 8589934592, 549755813888, -35184372088832, -4503599627370496, 1152921504606846976, 295147905179352825856, -75557863725914323419136, -38685626227668133590597632, 39614081257132168796771975168, 40564819207303340847894502572032, -41538374868278621028243970633760768, -85070591730234615865843651857942052864, 348449143727040986586495598010130648530944
Offset: 0
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[(-1)^Binomial(n+1,2)*2^Floor(n*(n+1)/4): n in [0..30]]; // G. C. Greubel, Feb 21 2018; Mar 18 2024
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Table[(-1)^Floor[(n+1)/2]*2^Floor[n*(n+1)/4], {n,0,30}] (* G. C. Greubel, Feb 21 2018; Mar 18 2024 *)
a[ n_] := (-1)^(n + Quotient[n, 4])*(-2)^Quotient[n (n + 1), 4]; (* Michael Somos, Mar 14 2020 *)
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for(n=0,30, print1((-1)^((n+1)\2)*2^(n*(n+1)\4), ", ")) \\ G. C. Greubel, Feb 21 2018; Mar 18 2024
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{a(n) = (-1)^(n + n\4) * (-2)^(n*(n+1)\4)}; /* Michael Somos, Mar 14 2020 */
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[(-1)^((n+1)//2)*2^(n*(n+1)//4) for n in range(31)] # G. C. Greubel, Mar 18 2024
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