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Place n equally spaced points on each side of a square, and join each of these points by a chord to the 3*n new points on the other three sides: sequence gives number of regions in the resulting planar graph.
5

%I #10 Nov 12 2023 02:11:55

%S 1,8,88,444,1544,3584,8356,14996,26572,42144,69988,93264,148364,

%T 196120,261536,347544,483056,572832,783252,907472,1141668,1413512,

%U 1775972,1958684,2466452,2897004,3384128,3852068,4733632,5042324,6263264,6869784,7878988,9014840,10035784,10909592,13109608

%N Place n equally spaced points on each side of a square, and join each of these points by a chord to the 3*n new points on the other three sides: sequence gives number of regions in the resulting planar graph.

%C See A367276 for further information.

%H Scott R. Shannon, <a href="/A367278/a367278.png">Image for n = 1</a>.

%H Scott R. Shannon, <a href="/A367278/a367278_1.png">Image for n = 2</a>.

%H Scott R. Shannon, <a href="/A367278/a367278_2.png">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A367278/a367278_3.png">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A367278/a367278_4.png">Image for n = 5</a>.

%H Scott R. Shannon, <a href="/A367278/a367278_5.png">Image for n = 9</a>.

%H Scott R. Shannon, <a href="/A367278/a367278_6.png">Image for n = 10</a>.

%F a(n) = A367279(n) - A367276(n) + 1 (Euler).

%Y Cf. A367276 (vertices), A367277 (interior vertices), A367279 (edges).

%K nonn

%O 0,2

%A _Scott R. Shannon_, Nov 11 2023