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A277279 Somos-4 sequence variant: a(n) = (a(n-1) * a(n-3) - a(n-2)^2) / a(n-4), a(0) = 1, a(1) = 1, a(2) = 2, a(3) = -1. 1

%I

%S 1,1,2,-1,-5,-11,-7,86,199,799,-4159,-17047,-155366,445015,7627979,

%T 81138437,142104721,-12357952274,-134098256401,-2117060496481,

%U 57564521075233,987319483194481,40297982292465650,-635283824578537969,-39106648195100243333

%N Somos-4 sequence variant: a(n) = (a(n-1) * a(n-3) - a(n-2)^2) / a(n-4), a(0) = 1, a(1) = 1, a(2) = 2, a(3) = -1.

%H Seiichi Manyama, <a href="/A277279/b277279.txt">Table of n, a(n) for n = 0..174</a>

%F a(n) = A210098(2*n + 1).

%F 0 = a(n)*a(n+4) - a(n+1)*a(n+3) + a(n+2)^2 for all n in Z.

%F 0 = a(n)*a(n+5) - a(n+1)*a(n+4) - 3*a(n+2)*a(n+3) for all n in Z.

%F 0 = a(n+1)^2*a(n+2)^2 - a(n)^2*a(n+3)^2 - a(n)*a(n+2)^3 - a(n+1)^3*a(n+3) - 2*a(n)*a(n+1)*a(n+2)*a(n+3) for all n in Z.

%F a(m) = -a(-1-n) for all n in Z. - _Michael Somos_, Mar 14 2020

%e G.f. = 1 + x + 2*x^2 - x^3 - 5*x^4 - 11*x^5 - 7*x^6 + 86*x^7 + 199*x^8 + ...

%t a[ n_] := a[n] = Which[ n < 0, -a[-1 - n], n < 3, 1 + Boole[n > 1], True, (a[n - 1] a[n - 3] - a[n - 2]^2) / a[n - 4]];

%t RecurrenceTable[{a[0]==a[1]==1,a[2]==2,a[3]==-1,a[n]==(a[n-1]a[n-3]-a[n-2]^2)/ a[n-4]},a,{n,30}] (* _Harvey P. Dale_, Nov 28 2019 *)

%o (PARI) {a(n) = my(v, m); if( n<0, -a(-1 -n), n<3, 1 + (n>1), v = vector( m=n+2, i, (-1)^(i<3) + (i==5)); for( i=6, m, v[i] = (v[i-1] * v[i-3] - v[i-2]^2) / v[i-4]); v[m])};

%Y Cf. A006720, A210098.

%K sign

%O 0,3

%A _Michael Somos_, Oct 08 2016

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Last modified August 12 23:52 EDT 2022. Contains 356077 sequences. (Running on oeis4.)