OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Cube Polynomial.
Eric Weisstein's World of Mathematics, Giraffe Graph.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 16*(29 - 10*n + n^2) for n >= 10.
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n >= 13.
G.f.: x*(-1-x-16*x^4+4*x^5-4*x^6-14*x^8-6*x^9+7*x^10-x^11)/(-1+x)^3.
MATHEMATICA
Table[n^2 + Ramp[n - 10]^2 + 4 Ramp[n - 9] Ramp[n - 6] + 4 Ramp[n - 5]^2 + 2 Ramp[n - 8] Ramp[n - 2] + 4 Ramp[n - 4] Ramp[n - 1], {n, 20}]
Join[{1, 4, 9, 16, 41, 80, 137, 212, 319}, LinearRecurrence[{3, -3, 1}, {464, 640, 848}, 11]]
CoefficientList[Series[(-1 - x - 16 x^4 + 4 x^5 - 4 x^6 - 14 x^8 - 6 x^9 + 7 x^10 - x^11)/(-1 + x)^3, {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 15 2026
STATUS
approved
