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A351153 Triangle read by rows: T(n, k) = n*(k - 1) - k*(k - 3)/2 with 0 < k <= n.

%I A351153 #21 Feb 16 2022 11:12:49
%S A351153 1,1,3,1,4,6,1,5,8,10,1,6,10,13,15,1,7,12,16,19,21,1,8,14,19,23,26,28,
%T A351153 1,9,16,22,27,31,34,36,1,10,18,25,31,36,40,43,45,1,11,20,28,35,41,46,
%U A351153 50,53,55,1,12,22,31,39,46,52,57,61,64,66,1,13,24,34,43,51,58,64,69,73,76,78
%N A351153 Triangle read by rows: T(n, k) = n*(k - 1) - k*(k - 3)/2 with 0 < k <= n.
%C A351153 Except for the number 2, it contains all the positive integers.
%F A351153 T(n, k) = 1 + Sum_{i=1..k-1} (n - i + 1).
%F A351153 From _R. J. Mathar_, Feb 07 2022: (Start)
%F A351153 G.f.: x*y*(1 - x + y*x^2 + y^2*x^3)/((1 - x)^2*(1 - y*x)^3).
%F A351153 T(n, k) = 1 + A141418(n+1, k-1) = 1 + A087401(n+1, k-1). (End)
%e A351153 Triangle begins:
%e A351153   1;
%e A351153   1, 3;
%e A351153   1, 4,  6;
%e A351153   1, 5,  8, 10;
%e A351153   1, 6, 10, 13, 15;
%e A351153   1, 7, 12, 16, 19, 21;
%e A351153   1, 8, 14, 19, 23, 26, 28;
%e A351153   ...
%t A351153 Flatten[Table[n(k-1)-k(k-3)/2,{n,12},{k,n}]]
%Y A351153 Cf. A000012 (1st column), A000217 (leading diagonal), A005843 (3rd column), A006007 (sum of the first n rows), A006527 (row sums).
%Y A351153 Cf. A087401, A141418, A351154.
%K A351153 nonn,easy,tabl
%O A351153 1,3
%A A351153 _Stefano Spezia_, Feb 02 2022