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

2,1

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).

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)

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 *)

Prog

(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

Crossrefs

Cf. A287430.

Sequence in context: A250586 A201853 A142843 * A012021 A175558 A289743

Adjacent sequences: A290754 A290755 A290756 * A290758 A290759 A290760

Keyword

nonn

Author

Eric W. Weisstein, Aug 09 2017

Extensions

Terms a(8) and beyond from Andrew Howroyd, Aug 31 2017

Status

approved