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
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Aug 09 2017
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, Aug 31 2017
STATUS
approved