OFFSET
1,4
COMMENTS
Sequence extended to a(1)-a(3) using the formula.
a(n) agrees with A243302(n-2) for 3 <= n <= 12.
LINKS
Eric Weisstein's World of Mathematics, Graph Circumference
Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).
FORMULA
a(n) = (3*n*(n + 1) - 14 - 4*cos(2*n*Pi/3) + 4*sqrt(3)*sin(2*n*Pi/3))/18.
a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n > 5.
G.f.: x^3*(-1 - x + x^2)/((-1 + x)^3*(1 + x + x^2)).
a(n) = floor((n+2)*(n-1)/6). - Stefanos Papanicolopulos, Dec 18 2020
E.g.f.: 1 + exp(-x/2)*(exp(3*x/2)*(3*x^2 + 6*x - 14) - 4*cos(sqrt(3)*x/2) + 4*sqrt(3)*sin(sqrt(3)*x/2))/18. - Stefano Spezia, Dec 18 2020
MATHEMATICA
Table[(3 n (n + 1) - 14 - 4 Cos[2 n Pi/3] + 4 Sqrt[3] Sin[2 n Pi/3])/18, {n, 20}]
LinearRecurrence[{2, -1, 1, -2, 1}, {0, 0, 1, 3, 4}, 20]
CoefficientList[Series[x^2 (-1 - x + x^2)/((-1 + x)^3 (1 + x + x^2)), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 25 2018
STATUS
approved