A392173 Total number of vertices in the graph (see A392172) formed when n points are placed in general position on each edge of a square and a chord is drawn from each point to the 3*n points on the other three sides.

4, 9, 82, 475, 1644, 4249, 9154, 17427, 30340, 49369, 76194, 112699, 160972, 223305, 302194, 400339, 520644, 666217, 840370, 1046619, 1288684, 1570489, 1896162, 2270035, 2696644, 3180729, 3727234, 4341307, 5028300, 5793769, 6643474, 7583379, 8619652, 9758665, 11006994, 12371419, 13858924, 15476697, 17232130, 19132819, 21186564, 23401369

Offset

0,1

Links

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

Scott R. Shannon, Illustration for a(1) = 9

Scott R. Shannon, Illustration for a(2) = 82

Scott R. Shannon, Illustration for a(3) = 475

Scott R. Shannon, Illustration for a(5) = 4249

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

Formula

a(n) = 4 + 4*n + (3/2)*n^2 - 9*n^3 + (17/2)*n^4.

From Stefano Spezia, Jan 03 2026: (Start)

G.f.: (4 - 11*x + 77*x^2 + 115*x^3 + 19*x^4)/(1 - x)^5.

E.g.f.: exp(x)*(8 + 10*x + 68*x^2 + 84*x^3 + 17*x^4)/2. (End)

Mathematica

A392173[n_] := n*(n*(n*(17*n - 18) + 3) + 8)/2 + 4; Array[A392173, 50, 0] (* or *)
LinearRecurrence[{5, -10, 10, -5, 1}, {4, 9, 82, 475, 1644}, 50] (* Paolo Xausa, Jan 03 2026 *)

Crossrefs

Cf. A392172 (regions), A392174 (edges), A334698, A365929, A331449.

Sequence in context: A082381 A155931 A309801 * A248245 A368629 A077530

Adjacent sequences: A392170 A392171 A392172 * A392174 A392175 A392176

Keyword

nonn,easy

Author

Scott R. Shannon and N. J. A. Sloane, Jan 02 2026

Status

approved