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A335074 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.

%I A335074 #18 May 22 2020 22:54:24
%S A335074 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 A335074 15,19,19,19,19,19,19,15,17,21,25,21,19,21,25,21,17,19,25,29,29,23,23,
%U A335074 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 A335074 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 A335074 The terms are from numeric computation - no formula for a(n) is currently known.
%H A335074 Scott R. Shannon, <a href="/A335074/a335074.png">Image for n = 3 showing the count of the vertices</a>.
%H A335074 Scott R. Shannon, <a href="/A335074/a335074_1.png">Image for n = 4 showing the count of the vertices</a>.
%H A335074 Scott R. Shannon, <a href="/A335074/a335074_2.png">Image for n = 7 showing the count of the vertices</a>.
%H A335074 Scott R. Shannon, <a href="/A335074/a335074_3.png">Image for n = 10 showing the count of the vertices</a>.
%H A335074 Scott R. Shannon, <a href="/A335074/a335074_4.png">Image for n = 12 showing the count of the vertices</a>.
%F A335074 Row sum n + Row sum A335056(n) = A159065(n).
%e A335074 Triangle begins:
%e A335074 1;
%e A335074 3, 3;
%e A335074 5, 3, 5;
%e A335074 7, 7, 7, 7;
%e A335074 9, 9, 7, 9, 9;
%e A335074 11, 13, 11, 11, 13, 11;
%e A335074 13, 15, 17, 11, 17, 15, 13;
%e A335074 15, 19, 19, 19, 19, 19, 19, 15;
%e A335074 17, 21, 25, 21, 19, 21, 25, 21, 17;
%e A335074 19, 25, 29, 29, 23, 23, 29, 29, 25, 19;
%e A335074 21, 27, 33, 33, 33, 23, 33, 33, 33, 27, 21;
%e A335074 23, 31, 37, 39, 39, 35, 35, 39, 39, 37, 31, 23;
%Y A335074 Cf. A335056, A159065, A331755, A333288, A306302.
%K A335074 nonn,tabl
%O A335074 2,2
%A A335074 _Scott R. Shannon_ and _N. J. A. Sloane_, May 22 2020