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 A182130 Number of independent sets of nodes in the armchair (3,3) carbon nanotube graph of breadth n (n>=1). 1
 27, 322, 4556, 61814, 847098, 11580788, 158413552, 2166639646, 29634348798, 405322443028, 5543789598764, 75825036741014, 1037095063081722, 14184841682767868, 194012817135153904, 2653605447140034790, 36294622054374551742, 496418784252960527212 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 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). 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). MATHEMATICA LinearRecurrence[{13, 17, -109, 42, 28}, {27, 322, 4556, 61814, 847098}, 20] (* Wesley Ivan Hurt, Oct 10 2021 *) PROG (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); CROSSREFS Sequence in context: A048396 A061181 A231911 * A224311 A224375 A010832 Adjacent sequences: A182127 A182128 A182129 * A182131 A182132 A182133 KEYWORD nonn,easy AUTHOR Cesar Bautista, Apr 13 2012 STATUS approved

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