A386486 a(0) = 1; thereafter a(n) = 4*n^2 - 3*n + 2.

1, 3, 12, 29, 54, 87, 128, 177, 234, 299, 372, 453, 542, 639, 744, 857, 978, 1107, 1244, 1389, 1542, 1703, 1872, 2049, 2234, 2427, 2628, 2837, 3054, 3279, 3512, 3753, 4002, 4259, 4524, 4797, 5078, 5367, 5664, 5969, 6282, 6603, 6932, 7269, 7614, 7967, 8328, 8697, 9074, 9459, 9852, 10253, 10662, 11079, 11504, 11937, 12378

Offset: 0

Author

N. J. A. Sloane, Aug 27 2025

Keywords

• nonn
• easy
• new

Comments

Differs from A001107, A054552, and A343560 only by a small constant, but has its own entry because of an important geometric application (which will be added soon).

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A001107, A054552, A343560.

Programs

Mathematica

A386486[n_] := If[n == 0, 1, (4*n - 3)*n + 2]; Array[A386486, 100, 0] (* or *)
LinearRecurrence[{3, -3, 1}, {1, 3, 12, 29}, 100] (* Paolo Xausa, Aug 27 2025 *)

Formula

From Elmo R. Oliveira, Sep 02 2025: (Start)

G.f.: (1 + 6*x^2 + x^3)/(1 - x)^3.

E.g.f.: exp(x)*(2 + x + 4*x^2) - 1.

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