A182130 Number of independent sets of nodes in the armchair (3,3) carbon nanotube graph of breadth n (n>=1).

27, 322, 4556, 61814, 847098, 11580788, 158413552, 2166639646, 29634348798, 405322443028, 5543789598764, 75825036741014, 1037095063081722, 14184841682767868, 194012817135153904, 2653605447140034790, 36294622054374551742, 496418784252960527212

Offset: 0

Author

Cesar Bautista, Apr 13 2012

Keywords

• nonn
• easy

Links

• Cesar Bautista, Table of n, a(n) for n = 0..500
• C. Bautista-Ramos and C. Guillen-Galvan, Fibonacci numbers of generalized Zykov sums, J. Integer Seq., 15 (2012), #12.7.8.
• Index entries for linear recurrences with constant coefficients, signature (13,17,-109,42,28).

Programs

Mathematica

LinearRecurrence[{13, 17, -109, 42, 28}, {27, 322, 4556, 61814,
847098}, 20] (* Wesley Ivan Hurt, Oct 10 2021 *)

Maxima

a[0]:27; a[1]:322; a[2]:4556; a[3]:61814; a[4]:847098;
a[n]:=13*a[n-1]+17*a[n-2]-109*a[n-3]+42*a[n-4]+28*a[n-5];
makelist(a[k],k,0,25);

Formula

a(n) = 13*a(n-1)+17*a(n-2)-109*a(n-3)+42*a(n-4)+28*a(n-5) with a(0)=27, a(1)=322, a(2)=4556, a(3)=61814, a(4)=847098.

G.f.: (27-29*x-89*x^2+55*x^3+28*x^4)/(1-13*x-17*x^2+109*x^3-42*x^4-28*x^5).