OFFSET
0,3
COMMENTS
Number of 5-cycles in the n-Dorogovtsev-Goltsev-Mendes graph (using the convention that DGM(0) = P_2).
LINKS
Eric Weisstein's World of Mathematics, Dorogovtsev-Goltsev-Mendes Graph.
Eric Weisstein's World of Mathematics, Graph Cycle.
Index entries for linear recurrences with constant coefficients, signature (6,-12,10,-3).
FORMULA
a(n) = 3/4*(3^(n + 1) - 2*n - 4*n^2 - 3).
a(n) = 6*a(n-1) - 12*a(n-2) + 10*a(n-3) - 3*a(n-4).
G.f.: 3*x^2*(1+3*x)/((-1+x)^3*(-1+3*x)).
MATHEMATICA
Table[3/4 (3^(n + 1) - 2 n - 4 n^2 - 3), {n, 0, 20}]
LinearRecurrence[{6, -12, 10, -3}, {0, 0, 3, 27}, 20]
CoefficientList[Series[3 x^2 (1 + 3 x)/((-1 + x)^3 (-1 + 3 x)), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Dec 06 2023
STATUS
approved