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A185160
Somos-4 variation with periodic coefficients.
1
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
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
KEYWORD
nonn
AUTHOR
Michael Somos, Dec 26 2012
STATUS
approved