OFFSET
0,1
COMMENTS
For n >= 1, also the number of (non-null) connected induced subgraphs in the n-book graph.
LINKS
Robert Israel, Table of n, a(n) for n = 0..1659
Eric Weisstein's World of Mathematics, Book Graph
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
Index entries for linear recurrences with constant coefficients, signature (9,-27,31,-12).
FORMULA
a(n) = 9*a(n-1) - 27*a(n-2) + 31*a(n-3) - 12*a(n-4).
G.f.: (3 - 14 x + 4 x^2 + 25 x^3)/((-1 + x)^2 (1 - 7 x + 12 x^2)).
From Stefano Spezia, May 30 2023: (Start)
E.g.f.: 2*exp(3*x) + exp(4*x) + 3*exp(x)*x. (End)
MAPLE
seq(2*3^n + 4^n + 3*n, n=0..30); # Robert Israel, Aug 09 2017
MATHEMATICA
Table[2 3^n + 4^n + 3 n, {n, 0, 20}]
LinearRecurrence[{9, -27, 31, -12}, {13, 40, 127, 430}, {0, 20}]
CoefficientList[Series[(3 - 14 x + 4 x^2 + 25 x^3)/((-1 + x)^2 (1 - 7 x + 12 x^2)), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 09 2017
STATUS
approved