This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383465 #40 Jul 24 2025 17:58:58
%S A383465 1,8,40,97,179,286,418,575,757,964,1196,1453,1735,2042,2374,2731,3113,
%T A383465 3520,3952,4409,4891,5398,5930,6487,7069,7676,8308,8965,9647,10354,
%U A383465 11086,11843,12625,13432,14264,15121,16003,16910,17842,18799,19781,20788,21820,22877,23959,25066,26198,27355,28537,29744,30976,32233,33515,34822
%N A383465 a(n) = 25*n^2/2 - 11*n/2 + 1.
%C A383465 David O. H. Cutler (paper in preparation) defines a 5-chain to be a planar graph consisting of a continuous path made up of five straight segments. Then a(n) is the maximum number of pieces that the plane can be divided into by drawing n 5-chains.
%C A383465 Related to maximum number of regions that can be obtained in the plane by drawing n pentagrams.
%H A383465 N. J. A. Sloane, <a href="/A383465/a383465.jpg">Illustration for n=1: a 5-chain that divides the plane into a(1) = 8 regions.</a> Two of the line segments are infinite.
%H A383465 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A383465 G.f.: (19*x^2+5*x+1)/(1-x)^3. - _Alois P. Heinz_, Jul 16 2025
%t A383465 a[n_]:= 25*n^2/2 - 11*n/2 + 1;Array[a,54,0] (* or *) LinearRecurrence[{3,-3,1},{1,8,40},54] (* or *) CoefficientList[Series[(19*x^2+5*x+1)/(1-x)^3,{x,0,53}],x] (* _James C. McMahon_, Jul 16 2025 *)
%Y A383465 A row of the array in A386478.
%K A383465 nonn,easy
%O A383465 0,2
%A A383465 _N. J. A. Sloane_, Jul 16 2025