A392174 - OEIS

%I #20 Jan 11 2026 09:22:33

%S 1,4,44,247,841,2156,4624,8779,15257,24796,38236,56519,80689,111892,

%T 151376,200491,260689,333524,420652,523831,644921,785884,948784,

%U 1135787,1349161,1591276,1864604,2171719,2515297,2898116,3323056,3793099,4311329,4880932,5505196,6187511,6931369,7740364,8618192,9568651,10595641,11703164

%N 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.

%H Paolo Xausa, <a href="/A392174/b392174.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

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

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

%F From _Stefano Spezia_, Jan 03 2026: (Start)

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

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

%t A392174[n_] := n^2*(n*(17*n - 18) + 9)/4 + n + 1; Array[A392174, 50, 0] (* or *)

%t LinearRecurrence[{5, -10, 10, -5, 1}, {1, 4, 44, 247, 841}, 50] (* _Paolo Xausa_, Jan 03 2026 *)

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

%K nonn,easy

%O 0,2

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 02 2026