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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

%I #31 Mar 28 2024 16:12:22

%S 27,322,4556,61814,847098,11580788,158413552,2166639646,29634348798,

%T 405322443028,5543789598764,75825036741014,1037095063081722,

%U 14184841682767868,194012817135153904,2653605447140034790,36294622054374551742,496418784252960527212

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

%H Cesar Bautista, <a href="/A182130/b182130.txt">Table of n, a(n) for n = 0..500</a>

%H C. Bautista-Ramos and C. Guillen-Galvan, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Bautista/bautista4.html">Fibonacci numbers of generalized Zykov sums</a>, J. Integer Seq., 15 (2012), #12.7.8.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (13,17,-109,42,28).

%F 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.

%F 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).

%t LinearRecurrence[{13, 17, -109, 42, 28}, {27, 322, 4556, 61814,

%t 847098}, 20] (* _Wesley Ivan Hurt_, Oct 10 2021 *)

%o (Maxima) a[0]:27; a[1]:322; a[2]:4556; a[3]:61814; a[4]:847098;

%o a[n]:=13*a[n-1]+17*a[n-2]-109*a[n-3]+42*a[n-4]+28*a[n-5];

%o makelist(a[k],k,0,25);

%K nonn,easy

%O 0,1

%A _Cesar Bautista_, Apr 13 2012

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Last modified July 25 03:24 EDT 2024. Contains 374586 sequences. (Running on oeis4.)