A206723 a(n) = 7*( ((3 + sqrt(5))/2)^n + ((3 - sqrt(5))/2)^n - 2 ).

7, 35, 112, 315, 847, 2240, 5887, 15435, 40432, 105875, 277207, 725760, 1900087, 4974515, 13023472, 34095915, 89264287, 233696960, 611826607, 1601782875, 4193522032, 10978783235, 28742827687, 75249699840, 197006271847, 515769115715, 1350301075312, 3535134110235, 9255101255407, 24230169656000, 63435407712607, 166076053481835, 434792752732912

Offset: 1

Author

N. J. A. Sloane, Feb 11 2012

Keywords

• nonn
• easy

Links

• Hang Gu and Robert M. Ziff, Crossing on hyperbolic lattices, arXiv preprint arXiv:1111.5626, 2011
• Index entries for linear recurrences with constant coefficients, signature (4,-4,1).

Crossrefs

Equals 7*A004146 for n >= 1.

Programs

Mathematica

LinearRecurrence[{4, -4, 1}, {7, 35, 112}, 33]  (* Jean-François Alcover, Sep 21 2017 *)

Formula

G.f.: -7*x*(1+x) / ( (x-1)*(x^2-3*x+1) ). - R. J. Mathar, Nov 15 2013