A185160 Somos-4 variation with periodic coefficients.

1, 1, 1, 1, 2, 5, 9, 61, 193, 1439, 13892, 121853, 1908467, 47166783, 675904139, 39429369055, 1213855360958, 67750536841003, 6132239054249611, 493982993144750867, 58550607494335286859, 14200800262701050362129, 1702987663133991103090484

Offset

0,5

Comments

Hone, et.al. page 8 gives the sequence denoted by tau_n.

Links

G. C. Greubel, Table of n, a(n) for n = 0..132

A. N. W. Hone, P. H. van der Kamp, G. R. W. Quispel, D. T. Tan, Integrability of reductions of the discrete KdV and potential KdV equations, 2012, arXiv:1211.6958 [nlin.SI], 2012-2013.

Formula

a(0) = a(1) = a(2) = a(3) = 1, a(n+4)*a(n) = c(n)*a(n+3)*a(n+1) + a(n+2)^2, c(0) = 2, c(1) = 1, c(n+2)=c(n).

Mathematica

c[n_]:= (3 + (-1)^n)/2; RecurrenceTable[{a[n] == (c[n - 3]*a[n - 1]*a[n - 3] + a[n - 2]^2)/a[n - 4], a[0] == 1, a[1] == 1, a[2] == 1, a[3] == 1}, a, {n, 0, 20}] (* G. C. Greubel, Aug 10 2018 *)

Prog

(PARI) {a(n) = if( n<0, (a(n+2)^2 + if(n%2, 2, 1)*a(n+1)*a(n+3))/a(n+4), if( n<4, 1, (a(n-2)^2 + if(n%2, 2, 1)*a(n-1)*a(n-3))/a(n-4) ))}
(Magma) /* By recurrence: */ c:=func<n | IsEven(n) select 2 else 1>; [n le 4 select 1 else (c(n)*Self(n-1)*Self(n-3)+Self(n-2)^2)/Self(n-4): n in [1..23]]; // Bruno Berselli, Dec 27 2012

Crossrefs

Sequence in context: A249583 A109469 A334986 * A289942 A239899 A188948

Adjacent sequences: A185157 A185158 A185159 * A185161 A185162 A185163

Keyword

nonn

Author

Michael Somos, Dec 26 2012

Status

approved