cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A182130 #31 Mar 28 2024 16:12:22
%S A182130 27,322,4556,61814,847098,11580788,158413552,2166639646,29634348798,
%T A182130 405322443028,5543789598764,75825036741014,1037095063081722,
%U A182130 14184841682767868,194012817135153904,2653605447140034790,36294622054374551742,496418784252960527212
%N A182130 Number of independent sets of nodes in the armchair (3,3) carbon nanotube graph of breadth n (n>=1).
%H A182130 Cesar Bautista, <a href="/A182130/b182130.txt">Table of n, a(n) for n = 0..500</a>
%H A182130 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 A182130 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (13,17,-109,42,28).
%F A182130 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 A182130 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 A182130 LinearRecurrence[{13, 17, -109, 42, 28}, {27, 322, 4556, 61814,
%t A182130 847098}, 20] (* _Wesley Ivan Hurt_, Oct 10 2021 *)
%o A182130 (Maxima) a[0]:27; a[1]:322; a[2]:4556; a[3]:61814; a[4]:847098;
%o A182130 a[n]:=13*a[n-1]+17*a[n-2]-109*a[n-3]+42*a[n-4]+28*a[n-5];
%o A182130 makelist(a[k],k,0,25);
%K A182130 nonn,easy
%O A182130 0,1
%A A182130 _Cesar Bautista_, Apr 13 2012