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
A183896
Imaginary part of a (-4,-4) Gaussian integer Somos-4 sequence.
Original entry on oeis.org
0, -1, -2, 0, 0, -128, -1024, 0, 0, -4194304, -134217728, 0, 0, -35184372088832, -4503599627370496, 0, 0, -75557863725914323419136, -38685626227668133590597632, 0, 0, -41538374868278621028243970633760768, -85070591730234615865843651857942052864, 0
Offset: 0
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[((-1)^Floor((n+1)/2) -1)*2^Floor((n^2+n-4)/4): n in [0..30]]; // G. C. Greubel, Mar 23 2024
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Table[((-1)^Floor[(n+1)/2] -1)*2^(Floor[n*(n+1)/4] -1), {n,0,30}] (* G. C. Greubel, Mar 23 2024 *)
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[((-1)^((n+1)//2) -1)*2^(n*(n+1)//4 -1) for n in range(31)] # G. C. Greubel, Mar 23 2024
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