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Number of independent sets of nodes in graph K_7 X C_n (n > 2).
2

%I #27 Dec 30 2023 23:48:12

%S 8,1,57,358,2605,18551,132504,946037,6754805,48229630,344362257,

%T 2458765387,17555720008,125348805401,894997357857,6390330310358,

%U 45627309530405,325781497023151,2326097788692504,16608466017870637,118585359913787005,846705985414379630

%N Number of independent sets of nodes in graph K_7 X C_n (n > 2).

%H Colin Barker, <a href="/A051932/b051932.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,8,1).

%F a(n) = 6*a(n-1) + 8*a(n-2) + a(n-3).

%F G.f.: (13*x^2+47*x-8)/(x^3+8*x^2+6*x-1). - _Harvey P. Dale_, Sep 11 2011

%t LinearRecurrence[{6,8,1},{8,1,57},20] (* _Harvey P. Dale_, Sep 11 2011 *)

%o (PARI) Vec((8 - 47*x - 13*x^2) / ((1 + x)*(1 - 7*x - x^2)) + O(x^30)) \\ _Colin Barker_, May 11 2017

%Y Row 7 of A287376.

%K easy,nonn

%O 0,1

%A _Stephen G Penrice_, Dec 19 1999

%E More terms from _James A. Sellers_, Dec 20 1999

%E Corrected by _T. D. Noe_, Nov 07 2006