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A290757 Number of (non-null) connected induced subgraphs in the (2 n)-crossed prism graph.

%I A290757 #17 Feb 16 2025 08:33:50
%S A290757 167,1666,14861,125972,1034803,8313830,65687321,512243704,3952731839,
%T A290757 30238302794,229652377381,1733456444636,13015423731275,97276566448558,
%U A290757 724116167445041,5371074588248768,39713352030673111,292804273605231122,2153305580970250301
%N A290757 Number of (non-null) connected induced subgraphs in the (2 n)-crossed prism graph.
%H A290757 Andrew Howroyd, <a href="/A290757/b290757.txt">Table of n, a(n) for n = 2..200</a>
%H A290757 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>
%H A290757 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CrossedPrismGraph.html">Crossed Prism Graph</a>
%H A290757 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</a>
%H A290757 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (16, -78, 112, -49).
%F A290757 From _Andrew Howroyd_, Aug 31 2017: (Start)
%F A290757 a(n) = 7^n + n*(191*7^(n-2) - 14)/3.
%F A290757 a(n) = 16*a(n-1) - 78*a(n-2) + 112*a(n-3) - 49*a(n-4) for n > 5.
%F A290757 G.f.: x^2*(167 - 1006*x + 1231*x^2 - 560*x^3)/((1 - x)^2 * (1 - 7*x)^2).
%F A290757 (End)
%t A290757 DeleteCases[#, 0] &@ CoefficientList[Series[x^2*(167 - 1006 x + 1231 x^2 - 560 x^3)/((1 - x)^2*(1 - 7 x)^2), {x, 0, 20}], x] (* _Michael De Vlieger_, Aug 31 2017 *)
%t A290757 a[n_] := (1/21)*(191*7^(n-1)*(n-1) - 98*(n-1) + 338*7^(n-1) - 98);
%t A290757 Table[a[n], {n, 2, 30}] (* _Jean-François Alcover_, Nov 08 2017, after _Andrew Howroyd_ *)
%t A290757 LinearRecurrence[{16, -78, 112, -49}, {167, 1666, 14861, 125972}, 20] (* _Eric W. Weisstein_, Jan 13 2018 *)
%o A290757 (PARI) Vec((167 - 1006*x + 1231*x^2 - 560*x^3)/((1 - x)^2 * (1 - 7*x)^2) + O(x^30)) \\ _Andrew Howroyd_, Aug 31 2017
%Y A290757 Cf. A287430.
%K A290757 nonn
%O A290757 2,1
%A A290757 _Eric W. Weisstein_, Aug 09 2017
%E A290757 Terms a(8) and beyond from _Andrew Howroyd_, Aug 31 2017