%I #23 May 11 2017 07:35:52

%S 1,29,477,8303,143697,2488431,43089985,746156517,12920616493,

%T 223736359029,3874270087045,67087749098875,1161706844818941,

%U 20116382073294655,348339884131004417,6031933298656980345,104450339960964929961,1808686034441106749965

%N Number of independent sets of nodes in graph C_7 x P_n (n>=0).

%H Cesar Bautista, <a href="/A182014/b182014.txt">Table of n, a(n) for n = 0..399</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_05">Index entries for linear recurrences with constant coefficients</a>, signature (17,8,-44,5,1).

%F a(n) = 17*a(n-1) + 8*a(n-2) - 44*a(n-3) + 5*a(n-4) + a(n-5) with a(0)=1, a(1)=29, a(2)=477, a(3)=8303, a(4)=143697.

%F G.f.: (x^4+6*x^3-24*x^2+12*x+1)/(-x^5-5*x^4+44*x^3-8*x^2-17*x+1).

%t LinearRecurrence[{17,8,-44,5,1},{1,29,477,8303,143697},30] (* _Harvey P. Dale_, Aug 27 2012 *)

%o (PARI) Vec((x^4+6*x^3-24*x^2+12*x+1)/(-x^5-5*x^4+44*x^3-8*x^2-17*x+1)+O(x^99)) \\ _Charles R Greathouse IV_, Apr 06 2012

%Y Row 7 of A286513.

%K nonn,easy

%O 0,2

%A _Cesar Bautista_, Apr 06 2012