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%I A287327 #23 Jan 14 2018 18:24:14
%S A287327 2,7,35,196,1127,6517,37730,218491,1265327,7327852,42437675,245768761,
%T A287327 1423317602,8242841887,47736669995,276456796756,1601040887327,
%U A287327 9272088633997,53697334226690,310976719148851,1800955694455127,10429852827143932,60402279928821635
%N A287327 Number of independent vertex sets (and vertex covers) in the 2n-crossed prism graph.
%C A287327 Sequence extrapolated to n = 0 using recurrence.
%H A287327 Andrew Howroyd, <a href="/A287327/b287327.txt">Table of n, a(n) for n = 0..200</a>
%H A287327 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CrossedPrismGraph.html">Crossed Prism Graph</a>
%H A287327 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>
%H A287327 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/VertexCover.html">Vertex Cover</a>
%H A287327 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7, -7).
%F A287327 a(n) = 7*a(n-1) - 7*a(n-2) for n > 1.
%F A287327 G.f.: (2 - 7*x)/(1 - 7*x + 7*x^2).
%t A287327 CoefficientList[Series[(2 - 7 x)/(1 - 7 x + 7 x^2), {x, 0, 22}], x] (* _Michael De Vlieger_, Aug 31 2017 *)
%t A287327 Table[(1/2 (7 - Sqrt[21]))^n + (1/2 (7 + Sqrt[21]))^n, {n, 0, 20}] // Expand (* _Eric W. Weisstein_, Sep 21 2017 *)
%t A287327 LinearRecurrence[{7, -7}, {7, 35}, {0, 20}] (* _Eric W. Weisstein_, Sep 21 2017 *)
%o A287327 (PARI) Vec((2 - 7*x)/(1 - 7*x + 7*x^2) + O(x^30))
%Y A287327 Cf. A276225 (maximal independent vertex sets), A287062, A290708.
%K A287327 nonn
%O A287327 0,1
%A A287327 _Andrew Howroyd_, Aug 31 2017

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