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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
1, 1, 2, -1, -5, -11, -7, 86, 199, 799, -4159, -17047, -155366, 445015, 7627979, 81138437, 142104721, -12357952274, -134098256401, -2117060496481, 57564521075233, 987319483194481, 40297982292465650, -635283824578537969, -39106648195100243333 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..174

FORMULA

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

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

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

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.

a(m) = -a(-1-n) for all n in Z. - Michael Somos, Mar 14 2020

EXAMPLE

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

MATHEMATICA

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]];

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 *)

PROG

(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])};

CROSSREFS

Cf. A006720, A210098.

Sequence in context: A222680 A110352 A107310 * A049950 A095216 A307258

Adjacent sequences:  A277276 A277277 A277278 * A277280 A277281 A277282

KEYWORD

sign

AUTHOR

Michael Somos, Oct 08 2016

STATUS

approved

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Last modified August 15 16:02 EDT 2020. Contains 336505 sequences. (Running on oeis4.)