A290757 Number of (non-null) connected induced subgraphs in the (2 n)-crossed prism graph.
167, 1666, 14861, 125972, 1034803, 8313830, 65687321, 512243704, 3952731839, 30238302794, 229652377381, 1733456444636, 13015423731275, 97276566448558, 724116167445041, 5371074588248768, 39713352030673111, 292804273605231122, 2153305580970250301
Offset: 2
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 2..200
- Eric Weisstein's World of Mathematics, Connected Graph
- Eric Weisstein's World of Mathematics, Crossed Prism Graph
- Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
- Index entries for linear recurrences with constant coefficients, signature (16, -78, 112, -49).
Crossrefs
Cf. A287430.
Programs
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Mathematica
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 *) a[n_] := (1/21)*(191*7^(n-1)*(n-1) - 98*(n-1) + 338*7^(n-1) - 98); Table[a[n], {n, 2, 30}] (* Jean-François Alcover, Nov 08 2017, after Andrew Howroyd *) LinearRecurrence[{16, -78, 112, -49}, {167, 1666, 14861, 125972}, 20] (* Eric W. Weisstein, Jan 13 2018 *) -
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
Formula
From Andrew Howroyd, Aug 31 2017: (Start)
a(n) = 7^n + n*(191*7^(n-2) - 14)/3.
a(n) = 16*a(n-1) - 78*a(n-2) + 112*a(n-3) - 49*a(n-4) for n > 5.
G.f.: x^2*(167 - 1006*x + 1231*x^2 - 560*x^3)/((1 - x)^2 * (1 - 7*x)^2).
(End)
Extensions
Terms a(8) and beyond from Andrew Howroyd, Aug 31 2017