OFFSET
1,1
COMMENTS
For n > 2, also the number of (non-null) connected induced subgraphs in the n-pan graph.
LINKS
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, Pan Graph
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).
FORMULA
a(n) = 3/2*(n^2 - n + 2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: -((3 x (1 - x + x^2))/(-1 + x)^3).
a(n) = 3*A000124(n-1). - R. J. Mathar, May 07 2024
MATHEMATICA
Table[3/2 (n^2 - n + 2), {n, 20}]
LinearRecurrence[{3, -3, 1}, {3, 6, 12}, 20]
CoefficientList[Series[-((3 (1 - x + x^2))/(-1 + x)^3), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 10 2017
STATUS
approved