A392174 One-fourth of the total number of edges 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.

1, 4, 44, 247, 841, 2156, 4624, 8779, 15257, 24796, 38236, 56519, 80689, 111892, 151376, 200491, 260689, 333524, 420652, 523831, 644921, 785884, 948784, 1135787, 1349161, 1591276, 1864604, 2171719, 2515297, 2898116, 3323056, 3793099, 4311329, 4880932, 5505196, 6187511, 6931369, 7740364, 8618192, 9568651, 10595641, 11703164

Offset

0,2

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) = (A392172(n) + A392173(n) - 1)/4 by Euler's formula.

a(n) = 1 + n + (9/4)*n^2 - (9/2)*n^3 + (17/4)*n^4.

From Stefano Spezia, Jan 03 2026: (Start)

G.f.: (1 - x + 34*x^2 + 57*x^3 + 11*x^4)/(1 - x)^5.

E.g.f.: exp(x)*(4 + 12*x + 74*x^2 + 84*x^3 + 17*x^4)/4. (End)

Mathematica

A392174[n_] := n^2*(n*(17*n - 18) + 9)/4 + n + 1; Array[A392174, 50, 0] (* or *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 4, 44, 247, 841}, 50] (* Paolo Xausa, Jan 03 2026 *)

Crossrefs

Cf. A392172 (regions), A392173 (vertices), A367122, A366932, A331448.

Sequence in context: A271294 A269907 A270130 * A074751 A129551 A202162

Adjacent sequences: A392171 A392172 A392173 * A392175 A392176 A392177

Keyword

nonn,easy

Author

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

Status

approved