OFFSET
1,1
COMMENTS
For n >= 3, also the number of Hamiltonian paths in the n-Plummer-Toft graph.
LINKS
Eric Weisstein's World of Mathematics, Hamiltonian Path.
Eric Weisstein's World of Mathematics, Plummer-Toft Graph.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: -4*x*(14-21*x+23*x^2)/(-1+x)^3.
E.g.f.: 4*(exp(x)*(8*x^2 - 9*x + 23) - 23). - Elmo R. Oliveira, Sep 04 2025
MATHEMATICA
Table[4 (23 - 17 n + 8 n^2), {n, 20}]
LinearRecurrence[{3, -3, 1}, {56, 84, 176}, 20]
CoefficientList[Series[-(4 (14 - 21 x + 23 x^2)/(-1 + x)^3), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 29 2025
STATUS
approved