A389626 One-third of the total number of edges formed after n points have been placed in general position on each edge of a triangle (as in A365929).

1, 3, 17, 85, 285, 731, 1573, 2997, 5225, 8515, 13161, 19493, 27877, 38715, 52445, 69541, 90513, 115907, 146305, 182325, 224621, 273883, 330837, 396245, 470905, 555651, 651353, 758917, 879285, 1013435, 1162381, 1327173, 1508897, 1708675, 1927665, 2167061, 2428093, 2712027, 3020165, 3353845, 3714441, 4103363, 4522057, 4972005, 5454725, 5971771

Offset

0,2

Comments

This is a companion to A366478.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = 3*n^4/2 - 2*n^3 + 3*n^2/2 + n + 1.

From Enrique Navarrete, Jan 01 2026: (Start)

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: (x + 1)*(5*x^3 + 15*x^2 - 3*x + 1)/(1 - x)^5.

E.g.f.: (1/2)*exp(x)*(3*x^4 + 14*x^3 + 12*x^2 + 4*x + 2). (End)

Maple

a389626:= n -> 3*n^4/2 - 2*n^3 + 3*n^2/2 + n + 1;

Mathematica

A389626[n_] := (n*(n - 2) + 2)*(n*(3*n + 2) + 1)/2; Array[A389626, 50, 0] (* or *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 3, 17, 85, 285}, 50] (* Paolo Xausa, Jan 03 2026 *)

Crossrefs

Cf. A365929, A366478, A366932, A367015.

Sequence in context: A225307 A318769 A344228 * A216681 A350456 A037787

Adjacent sequences: A389623 A389624 A389625 * A389627 A389628 A389629

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 01 2026

Status

approved