A256858 - OEIS

%I #32 Dec 17 2023 11:23:12

%S 1,1,1,1,0,1,-1,2,-3,3,-3,4,-2,8,9,17,29,50,83,107,56,239,-243,1103,

%T -2351,3775,-7227,14463,-18648,55283,54011,256666,698301,2059753,

%U 5324929,9820288,15128062,55075036,-28437275,503857819,-1438167267,4083736906

%N a(n) = (-a(n-1) * a(n-6) + a(n-2) * a(n-5)) / a(n-7) with a(n) = 1 if abs(n) < 4, a(11) = 4.

%C Similar to the Somos-6 and Somos-7 sequences with many bilinear identities.

%H G. C. Greubel, <a href="/A256858/b256858.txt">Table of n, a(n) for n = 0..416</a>

%F a(2*n - 5) = A102276(n) for all n in Z.

%F a(2*n) = A256916(n) for all n in Z.

%F a(n) = a(-n) for all n in Z.

%F 0 = a(n) * a(n+7) + a(n+1) * a(n+6) - a(n+2) * a(n+5) for all n in Z.

%F 0 = a(n) * a(n+8) - a(n+2) * a(n+6) - a(n+4)^2 + (2 - mod(n,2)) * a(n+3) * a(n+5) for all n in Z.

%F 0 = a(n) * a(n+11) + a(n+1) * a(n+10) + a(n+5) * a(n+6) for all n in Z. - _Michael Somos_, Apr 14 2015

%t Join[{1, 1, 1, 1, 0, 1, -1, 2, -3, 3, -3, 4}, RecurrenceTable[{a[n] == (-a[n - 1]*a[n - 6] + a[n - 2]*a[n - 5])/a[n - 7], a[12] == -2, a[13] == 8, a[14] == 9, a[15] == 17, a[16] == 29, a[17] == 50, a[18] == 83}, a, {n, 12, 60}]] (* _G. C. Greubel_, Aug 03 2018 *)

%t a[n_] := Which[n<0, a[-n], n<12, {1, 1, 1, 1, 0, 1, -1, 2, -3, 3, -3, 4}[[1+n]], True, a[n] = (-a[n-1]*a[n-6] + a[n-2]*a[n-5])/a[n-7]]; (* _Michael Somos_, Dec 16 2023 *)

%o (PARI) {a(n) = my(an); n = abs(n)+1; an = concat([ 1, 1, 1, 1, 0, 1, -1, 2, -3, 3, -3, 4], vector(max(0, n-12), k)); for(k=13, n, an[k] = (-an[k-1] * an[k-6] + an[k-2] * an[k-5]) / an[k-7]); an[n]};

%o (PARI) {a(n) = my(an); n = abs(n)+1; an = vector(n, k, 1); if( n>=5, an[5] = 0); if( n>=7, an[7] = -1); if( n>=8, an[8] = 2); for(k=9, n, an[k] = if( k==12, 4, (-an[k-1] * an[k-6] + an[k-2] * an[k-5]) / an[k-7])); an[n]};

%o (Magma) I:=[-2,8,9,17,29,50,83]; [1, 1, 1, 1, 0, 1, -1, 2, -3, 3, -3, 4] cat [n le 7 select I[n] else (-Self(n-1)*Self(n-6) + Self(n-2)*Self(n-5))/Self(n-7): n in [1..30]]; // _G. C. Greubel_, Aug 03 2018

%Y Cf. A102276, A256916.

%K sign

%O 0,8

%A _Michael Somos_, Apr 12 2015