A220839 Tropical version of the degree-6 recurrence x(n+6)*x(n) = (x(n+5)*x(n+1))^2 + x(n+4)^2*x(n+3)^4*x(n+2)^2.

-1, 0, 0, 0, 0, 0, 1, 2, 4, 8, 18, 38, 79, 164, 342, 712, 1482, 3084, 6417, 13356, 27794, 57840, 120366, 250484, 521263, 1084758, 2257402, 4697696, 9775996, 20344034, 42336321, 88102688, 183343368, 381541032, 793994136, 1652316880, 3438502815, 7155589680

Offset

1,8

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Allan Fordy and Andrew Hone, Discrete integrable systems and Poisson algebras from cluster maps, arXiv:1207.6072 [nlin.SI], 2012. See Example 3.7.

Formula

Empirical g.f.: -x*(x^7+x^6-x^4+x^3+2*x^2+x-1) / ((x-1)*(x^2+x+1)*(x^4-x^3-2*x^2-x+1)*(x^6+x^3+1)). - Colin Barker, Jul 22 2013

Mathematica

Join[{-1}, RecurrenceTable[{d[n + 6] + d[n] == Max[2*d[n + 5] + 2*d[n + 1], 2*d[n + 4] + 4*d[n + 3] + 2*d[n + 2]],  d[2] == 0, d[3] == 0, d[4] == 0, d[5] == 0, d[6] == 0, d[7] == 1}, d, {n, 2, 50}]] (* G. C. Greubel, Aug 10 2018 *)

Prog

(PARI) a=vector(99); a[1]= -1; a[2]=a[3]=a[4]=a[5]=a[6]=0; for(n=7, #a, a[n]=2*max(a[n-1]+a[n-5], a[n-2]+2*a[n-3]+a[n-4])-a[n-6]); a; \\ Michel Marcus, Feb 08 2013

Crossrefs

Sequence in context: A018096 A024415 A339158 * A288206 A371791 A218078

Adjacent sequences: A220836 A220837 A220838 * A220840 A220841 A220842

Keyword

sign

Author

N. J. A. Sloane, Dec 23 2012

Extensions

More terms from Michel Marcus, Feb 08 2013

Definition corrected by N. J. A. Sloane, Jan 11 2024 at the suggestion of Helmut Ruhland.

Status

approved