OFFSET
1,1
COMMENTS
a(n) is also the number of 4-cycles in the (n+1)-Dorogovtsev-Goltsev-Mendes graph (using the indexing convention that the 0-Dorogovtsev-Goltsev-Mendes graph is P_2). - Eric W. Weisstein, Dec 06 2023
LINKS
Eric Weisstein's World of Mathematics, Connected Graph.
Eric Weisstein's World of Mathematics, Dorogovtsev-Goltsev-Mendes Graph.
Eric Weisstein's World of Mathematics, Graph Cycle.
Eric Weisstein's World of Mathematics, King Graph.
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph.
Index entries for linear recurrences with constant coefficients, signature (5, -7, 3).
FORMULA
a(n) = 3/4*(3^(n + 1) - 2*n - 3).
a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3).
G.f.: -((3 x)/((-1 + x)^2 (-1 + 3 x))).
MATHEMATICA
Table[3/4 (3^(n + 1) - 2 n - 3), {n, 20}]
LinearRecurrence[{5, -7, 3}, {3, 15, 54}, 40]
CoefficientList[Series[-3/((-1 + x)^2 (-1 + 3 x)), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 10 2017
STATUS
approved