OFFSET
1,3
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, King Graph
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Colin Barker, Jun 19 2017: (Start)
G.f.: 2*x^3*(41 + 92*x - 7*x^2) / (1 - x)^3.
a(n) = 550 - 534*n + 126*n^2 for n > 2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 4. (End)
E.g.f.: 2*exp(x)*(275 - 204*x + 63*x^2) - 550 - 142*x + 7*x^2. - Stefano Spezia, Aug 14 2022
MATHEMATICA
Table[If[n < 3, 0, 2 (275 - 267 n + 63 n^2)], {n, 20}]
CoefficientList[Series[(2 x^2 (-41 - 92 x + 7 x^2))/(-1 + x)^3, {x, 0, 20}], x]
Join[{0, 0}, LinearRecurrence[{3, -3, 1}, {142, -14, 82}, {3, 20}]]
PROG
(PARI) concat(vector(2), Vec(2*x^3*(41 + 92*x - 7*x^2) / (1 - x)^3 + O(x^50))) \\ Colin Barker, Jun 19 2017
(PARI) a(n)=if(n>2, 126*n^2-534*n+550, 0) \\ Charles R Greathouse IV, Jun 19 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 19 2017
EXTENSIONS
More terms from Colin Barker, Jun 19 2017
STATUS
approved