A162547 Somos-4 variant: if n!=4k+1, then a(n) = (4*a(n-1)*a(n-3) - 4*a(n-2)^2) / a(n-4), otherwise a(n) = 0, with a(-2) = a(-1) = a(0) = 1.
1, 0, -4, -16, -64, 0, 4096, 65536, 1048576, 0, -1073741824, -68719476736, -4398046511104, 0, 72057594037927936, 18446744073709551616, 4722366482869645213696, 0, -1237940039285380274899124224, -1267650600228229401496703205376, -1298074214633706907132624082305024, 0
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..114
- Paul Barry, Invariant number triangles, eigentriangles and Somos-4 sequences, arXiv preprint arXiv:1107.5490 [math.CO], 2011.
- Paul Barry, On the Connection Coefficients of the Chebyshev-Boubaker polynomials, The Scientific World Journal, Volume 2013 (2013), Article ID 657806, 10 pages.
- Paul Barry, Riordan arrays, the A-matrix, and Somos 4 sequences, arXiv:1912.01126 [math.CO], 2019.
Programs
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Mathematica
a[ n_] := With[{m = n + 1, k = Quotient[n + 2, 4]}, Boole[Mod[m, 4] != 2] (-1)^k 4^(k (m - 2 k))]; (* Michael Somos, Jun 26 2017 *) -
PARI
{a(n) = my(m=n+1, k=(n+2)\4); (m%4!=2) * (-1)^k * 4^(k*(m - 2*k))}; /* Michael Somos, Jul 20 2014 */
Formula
a(n) = a(-2 - n), a(n) * a(n+5) = 4 * a(n+1) * a(n+4) for all n in Z. - Michael Somos, Jul 20 2014
a(4*n + 1) = 0 for all n in Z. - Michael Somos, Jun 26 2017
Comments