A038866 a(n) = (n+4)^3 - n^3.

124, 208, 316, 448, 604, 784, 988, 1216, 1468, 1744, 2044, 2368, 2716, 3088, 3484, 3904, 4348, 4816, 5308, 5824, 6364, 6928, 7516, 8128, 8764, 9424, 10108, 10816, 11548, 12304, 13084, 13888, 14716, 15568, 16444, 17344, 18268, 19216, 20188, 21184, 22204, 23248

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 12*n^2 + 48*n + 64. - Charles R Greathouse IV, Nov 12 2014

From Elmo R. Oliveira, Apr 21 2026: (Start)

G.f.: 4*x*(31 - 41*x + 16*x^2)/(1 - x)^3.

E.g.f.: 4*(-16 + (16 + 15*x + 3*x^2)*exp(x)).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

Mathematica

Table[64+48 n+12 n^2, {n, 40}] (* or *) #[[5]]-#[[1]]&/@Partition[Range[40]^3, 5, 1] (* Harvey P. Dale, Mar 01 2024 *)
(* Alternative: *)
LinearRecurrence[{3, -3, 1}, {124, 208, 316}, 40] (* Harvey P. Dale, Mar 01 2024 *)

Prog

(PARI) a(n)=12*n^2 + 48*n + 64 \\ Charles R Greathouse IV, Nov 12 2014

Crossrefs

Sequence in context: A133606 A372680 A270864 * A043367 A023740 A031476

Adjacent sequences: A038863 A038864 A038865 * A038867 A038868 A038869

Keyword

nonn,easy

Author

Jeff Burch

Extensions

More terms from Elmo R. Oliveira, Apr 21 2026

Status

approved