A355839 - OEIS

%I #10 Jul 20 2022 10:11:22

%S 5,25,133,357,1013,1637,3761,5561,9313,13065,21689,25357,41553,50157,

%T 66005,84897,117793,129841,181717,198857,251189,302293,383161,401073,

%U 517193,587041,687765,763425,949869,966249,1234425,1320913,1512233,1703657,1912765,2023569,2475361,2649813,2934997

%N Number of vertices formed in a square by straight line segments when connecting the n+1 points along each edge that divide it into n equal parts to the n+1 points on the edge on the opposite side of the square.

%C This sequence is similar to A355799 but here the corner vertices of the square are also connected to points on the opposite edge.

%H Scott R. Shannon, <a href="/A355839/a355839.png">Image for n = 2</a>.

%H Scott R. Shannon, <a href="/A355839/a355839_1.png">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A355839/a355839_2.png">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A355839/a355839_3.png">Image for n = 5</a>.

%H Scott R. Shannon, <a href="/A355839/a355839_4.png">Image for n = 6</a>.

%H Scott R. Shannon, <a href="/A355839/a355839_5.png">Image for n = 11</a>.

%F a(n) = A355840(n) - A355838(n) + 1 by Euler's formula.

%Y Cf. A355838 (regions), A355840 (edges), A355841 (k-gons), A355799 (without corner vertices), A290131, A331452, A335678.

%K nonn

%O 1,1

%A _Scott R. Shannon_, Jul 18 2022