OFFSET
1,2
COMMENTS
Sequence extended to a(1) using the formula.
LINKS
Eric Weisstein's World of Mathematics, Cube Polynomial.
Eric Weisstein's World of Mathematics, White Bishop Graph.
Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1).
FORMULA
a(n) = (n + 1)*(3*((-1)^n - 1) + n*(n + 1)*(n + 2))/24.
a(n) = 3*a(n-1)-a(n-2)-5*a(n-3)+5*a(n-4)+a(n-5)-3*a(n-6)+a(n-7).
G.f.: -x^2*(3+x^2)/((-1+x)^5*(1+x)^2).
MATHEMATICA
Table[(n + 1)*(3*((-1)^n - 1) + n*(n + 1)*(n + 2))/24, {n, 20}]
Table[Piecewise[{{n (n + 1)^2 (n + 2)/24, Mod[n, 2] == 0}, {(n - 1) (n + 1) (n^2 + 4 n + 6)/24, Mod[n, 2] == 1}}], {n, 20}]
LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {3, 9, 25, 51, 98, 166, 270}, 20]
CoefficientList[Series[-x (3 + x^2)/((-1 + x)^5 (1 + x)^2), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Mar 15 2026
STATUS
approved
