OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).
FORMULA
a(n) = floor(3*n^3+9*n^2/2+4*n+1).
a(2*n) = 24*n^3 + 18*n^2 + 8*n + 1.
a(2*n-1) = 24*n^3-18*n^2+8*n-2 for n > 0.
a(2*n) = A248575(2*n) + 4*n + 1.
a(2*n-1) = A248575(2*n-1) + 4*n - 2.
From Stefano Spezia, Jul 09 2024: (Start)
G.f.: (1 + 9*x + 17*x^2 + 7*x^3 + 2*x^3)/((1 - x)^4*(1 + x)).
E.g.f.: exp(x)*(1 + 11*x + 14*x^2 + 3*x^3). (End)
MATHEMATICA
Table[Floor[Sum[(n^3+k)^(1/3), {k, 0, 3n^2+3n+1}]], {n, 0, 40}] (* Stefano Spezia, Jul 07 2024 *)
PROG
(PARI) a(n) = 3*n^3+9*n^2\2+4*n+1; \\ Michel Marcus, Jul 09 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amrit Awasthi, Jul 07 2024
STATUS
approved