A386485 a(0) = 1; thereafter a(n) = 5*n^2 - 5*n + 2.

1, 2, 12, 32, 62, 102, 152, 212, 282, 362, 452, 552, 662, 782, 912, 1052, 1202, 1362, 1532, 1712, 1902, 2102, 2312, 2532, 2762, 3002, 3252, 3512, 3782, 4062, 4352, 4652, 4962, 5282, 5612, 5952, 6302, 6662, 7032, 7412, 7802, 8202, 8612, 9032, 9462, 9902, 10352, 10812, 11282, 11762, 12252, 12752, 13262, 13782, 14312

Offset: 0

Author

N. J. A. Sloane, Aug 18 2025

Keywords

• nonn
• easy
• changed

Comments

Maximum number of regions that can be formed in the plane by drawing n regular pentagons (of any size). Differs from A062786 and A124080 by a small constant shift, but is included here because of its geometrical applications.

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. A051890, A069894, A077588, A386480.

See also A062786, A124080.

Programs

Mathematica

A386485[n_] := If[n == 0, 1, 5*n*(n - 1) + 2]; Array[A386485, 60, 0] (* or *)
LinearRecurrence[{3, -3, 1}, {1, 2, 12, 32}, 60] (* Paolo Xausa, Aug 18 2025 *)

Formula

G.f.: -(x^3+9*x^2-x+1)/(x-1)^3.

From Elmo R. Oliveira, Sep 04 2025: (Start)

E.g.f.: exp(x)*(2 + 5*x^2) - 1.

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