Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 May 22 2020 10:39:17
%S 1,3,3,5,11,5,7,19,19,7,9,29,43,29,9,11,37,61,61,37,11,13,47,83,105,
%T 83,47,13,15,57,103,143,143,103,57,15,17,69,125,183,211,183,125,69,17,
%U 19,81,143,215,267,267,215,143,81,19,21,95,167,253,329,369,329,253,167,95,21,23,109,189,289,385,455,455,385,289,189,109,23
%N Triangle read by rows: consider a figure made up of a row of n congruent rectangles and the diagonals of all possible rectangles; T(n,k) (1 <= k <= n) is the number of vertices inside the k-th rectangle.
%C The terms are from numeric computation - no formula for a(n) is currently known.
%H Scott R. Shannon, <a href="/A335056/a335056.png">Image for n = 2 showing the count of the vertices</a>.
%H Scott R. Shannon, <a href="/A335056/a335056_1.png">Image for n = 3 showing the count of the vertices</a>.
%H Scott R. Shannon, <a href="/A335056/a335056_2.png">Image for n = 5 showing the count of the vertices</a>.
%H Scott R. Shannon, <a href="/A335056/a335056_3.png">Image for n = 9 showing the count of the vertices</a>.
%H Scott R. Shannon, <a href="/A335056/a335056_4.png">Image for n = 12 showing the count of the vertices</a>.
%F Row sum n + Row sum A335074(n) = A159065(n).
%e Triangle begins:
%e 1;
%e 3, 3;
%e 5, 11, 5;
%e 7, 19, 19, 7;
%e 9, 29, 43, 29, 9;
%e 11, 37, 61, 61, 37, 11;
%e 13, 47, 83, 105, 83, 47, 13;
%e 15, 57, 103, 143, 143, 103, 57, 15;
%e 17, 69, 125, 183, 211, 183, 125, 69, 17;
%e 19, 81, 143, 215, 267, 267, 215, 143, 81, 19;
%e 21, 95, 167, 253, 329, 369, 329, 253, 167, 95, 21;
%e 23, 109, 189, 289, 385, 455, 455, 385, 289, 189, 109, 23;
%e 25, 125, 215, 331, 451, 551, 597, 551, 451, 331, 215, 125, 25;
%Y Cf. A335074, A159065, A331755, A333288, A306302.
%K nonn,tabl
%O 1,2
%A _Scott R. Shannon_ and _N. J. A. Sloane_, May 21 2020