|
%I #25 Sep 13 2023 12:21:19
%S 4,1,13,34,121,391,1300,4285,14161,46762,154453,510115,1684804,
%T 5564521,18378373,60699634,200477281,662131471,2186871700,7222746565,
%U 23855111401,78788080762,260219353693,859446141835,2838557779204,9375119479441,30963916217533
%N Number of independent sets of vertices in graph K_3 X C_n (n > 2).
%H Colin Barker, <a href="/A051928/b051928.txt">Table of n, a(n) for n = 0..1000</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_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,1).
%F a(n) = 2*a(n-1) + 4*a(n-2) + a(n-3).
%F G.f.: (4-7*x-5*x^2)/((1+x)*(1-3*x-x^2)). - _Colin Barker_, May 22 2012
%F a(n) = 2*(-1)^n + ((3-sqrt(13))/2)^n + ((3+sqrt(13))/2)^n. - _Colin Barker_, May 11 2017
%F a(n) = A006497+2*(-1)^n. - _R. J. Mathar_, Oct 20 2017
%t LinearRecurrence[{2,4,1},{4,1,13},30] (* _Harvey P. Dale_, Nov 20 2021 *)
%o (PARI) Vec((4-7*x-5*x^2)/((1+x)*(1-3*x-x^2)) + O(x^30)) \\ _Colin Barker_, May 11 2017
%Y Row 3 of A287376.
%K easy,nonn
%O 0,1
%A _Stephen G Penrice_, Dec 19 1999
|
