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A182141 Number of independent sets of nodes in the armchair (3,3) carbon nanotorus graph of breadth n (n>=1). 1

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

%S 27,18,322,2787,37730,486773,6616216,89809934,1226678898,16759965210,

%T 229174768672,3134027776854,42863602781324,586250943722267,

%U 8018366958787066,109670557564651352,1500014136347328018,20516391520781511387,280612359537735848734

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

%H Cesar Bautista, <a href="/A182141/b182141.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), Article 12.7.8.

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (8,-1,-1018,1836,20616,-43461,-185682,384405,762090,-1499721,-1538730, 2873116,1499424,-2714609,-574862,1107300,18144,-108864).

%F a(n) = 18*a(n-1) -a(n-2) -1018*a(n-3) +1836*a(n-4) +20616*a(n-5) -43461*a(n-6) -185682*a(n-7) +384405*a(n-8) +762090*a(n-9) -1499721*a(n-10) -1538730*a(n-11) +2873116*a(n-12) +1499424*a(n-13) -2714609*a(n-14) -574862*a(n-15) +1107300*a(n-16) +18144*a(n-17) -108864*a(n-18).

%F G.f.: (979776*x^18 -75600*x^17 -12197940*x^16 +5916552*x^15 +35833019*x^14 -19220271*x^13 -44070216*x^12 +23310438*x^11 +26177559*x^10 -13274349*x^9 -7520073*x^8 +3654387*x^7 +940365*x^6 -451464*x^5 -43362*x^4 +24495*x^3 +25*x^2 -468*x+27)/( (x-1) *(x+1) *(3*x^3-5*x^2-5*x+1) *(36*x^4-x^3-20*x^2-x+1) *(36*x^4+x^3-20*x^2+x+1) *(28*x^5+42*x^4-109*x^3+17*x^2+13*x-1)).

%o (Maxima) a[0]:27; a[1]:18; a[2]:322; a[3]:2787; a[4]:37730; a[5]:486773; a[6]:6616216; a[7]:89809934; a[8]:1226678898; a[9]:16759965210; a[10]:229174768672; a[11]:3134027776854; a[12]:42863602781324; a[13]:586250943722267; a[14]:8018366958787066; a[15]:109670557564651352; a[16]:1500014136347328018; a[17]:20516391520781511387; a[18]:280612359537735848734;

%o a[n]:=18*a[n-1]-a[n-2]-1018*a[n-3]+1836*a[n-4]+20616*a[n-5]-43461*a[n-6]-185682*a[n-7]+384405*a[n-8]+762090*a[n-9]-1499721*a[n-10]-1538730*a[n-11]+2873116*a[n-12]+1499424*a[n-13]-2714609*a[n-14]-574862*a[n-15]+1107300*a[n-16]+18144*a[n-17]-108864*a[n-18];

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

%K nonn,easy

%O 0,1

%A _Cesar Bautista_, Apr 14 2012

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Last modified July 16 05:19 EDT 2024. Contains 374343 sequences. (Running on oeis4.)