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A355859 Triangle read by rows: T(n,k) = (n + k)/2 if (n + k) is congruent to 0 (mod 2), otherwise T(n,k) = 0; n >= 1, k >= 1.

%I A355859 #14 Jul 21 2022 03:11:02
%S A355859 1,0,2,2,0,3,0,3,0,4,3,0,4,0,5,0,4,0,5,0,6,4,0,5,0,6,0,7,0,5,0,6,0,7,
%T A355859 0,8,5,0,6,0,7,0,8,0,9,0,6,0,7,0,8,0,9,0,10,6,0,7,0,8,0,9,0,10,0,11,0,
%U A355859 7,0,8,0,9,0,10,0,11,0,12,7,0,8,0,9,0,10,0,11,0,12,0,13,0
%N A355859 Triangle read by rows: T(n,k) = (n + k)/2 if (n + k) is congruent to 0 (mod 2), otherwise T(n,k) = 0; n >= 1, k >= 1.
%C A355859 Row sums see A001318.
%e A355859 The triangle begins:
%e A355859       k=1  2  3  4  5  6
%e A355859   n=1:  1;
%e A355859   n=2:  0, 2;
%e A355859   n=3:  2, 0, 3;
%e A355859   n=4:  0, 3, 0, 4;
%e A355859   n=5:  3, 0, 4, 0, 5;
%e A355859   n=6:  0, 4, 0, 5, 0, 6;
%e A355859   and so on.
%t A355859 T[n_, k_] := If[EvenQ[n + k], (n + k)/2, 0]; Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* _Amiram Eldar_, Jul 19 2022 *)
%Y A355859 Cf. A001318, A138099 (without the zeros).
%K A355859 nonn,tabl
%O A355859 1,3
%A A355859 _Ctibor O. Zizka_, Jul 19 2022