A335074 - OEIS

%I #18 May 22 2020 22:54:24

%S 1,3,3,5,3,5,7,7,7,7,9,9,7,9,9,11,13,11,11,13,11,13,15,17,11,17,15,13,

%T 15,19,19,19,19,19,19,15,17,21,25,21,19,21,25,21,17,19,25,29,29,23,23,

%U 29,29,25,19,21,27,33,33,33,23,33,33,33,27,21,23,31,37,39,39,35,35,39,39,37,31,23

%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-1) is the number of vertices on the edge separating rectangles k and k+1.

%C The terms are from numeric computation - no formula for a(n) is currently known.

%H Scott R. Shannon, <a href="/A335074/a335074.png">Image for n = 3 showing the count of the vertices</a>.

%H Scott R. Shannon, <a href="/A335074/a335074_1.png">Image for n = 4 showing the count of the vertices</a>.

%H Scott R. Shannon, <a href="/A335074/a335074_2.png">Image for n = 7 showing the count of the vertices</a>.

%H Scott R. Shannon, <a href="/A335074/a335074_3.png">Image for n = 10 showing the count of the vertices</a>.

%H Scott R. Shannon, <a href="/A335074/a335074_4.png">Image for n = 12 showing the count of the vertices</a>.

%F Row sum n + Row sum A335056(n) = A159065(n).

%e Triangle begins:

%e 1;

%e 3, 3;

%e 5, 3, 5;

%e 7, 7, 7, 7;

%e 9, 9, 7, 9, 9;

%e 11, 13, 11, 11, 13, 11;

%e 13, 15, 17, 11, 17, 15, 13;

%e 15, 19, 19, 19, 19, 19, 19, 15;

%e 17, 21, 25, 21, 19, 21, 25, 21, 17;

%e 19, 25, 29, 29, 23, 23, 29, 29, 25, 19;

%e 21, 27, 33, 33, 33, 23, 33, 33, 33, 27, 21;

%e 23, 31, 37, 39, 39, 35, 35, 39, 39, 37, 31, 23;

%Y Cf. A335056, A159065, A331755, A333288, A306302.

%K nonn,tabl

%O 2,2

%A _Scott R. Shannon_ and _N. J. A. Sloane_, May 22 2020