A351153 - OEIS

%I #21 Feb 16 2022 11:12:49

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

%C Except for the number 2, it contains all the positive integers.

%F T(n, k) = 1 + Sum_{i=1..k-1} (n - i + 1).

%F From _R. J. Mathar_, Feb 07 2022: (Start)

%F G.f.: x*y*(1 - x + y*x^2 + y^2*x^3)/((1 - x)^2*(1 - y*x)^3).

%F T(n, k) = 1 + A141418(n+1, k-1) = 1 + A087401(n+1, k-1). (End)

%e Triangle begins:

%e   1;

%e   1, 3;

%e   1, 4,  6;

%e   1, 5,  8, 10;

%e   1, 6, 10, 13, 15;

%e   1, 7, 12, 16, 19, 21;

%e   1, 8, 14, 19, 23, 26, 28;

%e   ...

%t Flatten[Table[n(k-1)-k(k-3)/2,{n,12},{k,n}]]

%Y Cf. A000012 (1st column), A000217 (leading diagonal), A005843 (3rd column), A006007 (sum of the first n rows), A006527 (row sums).

%Y Cf. A087401, A141418, A351154.

%K nonn,easy,tabl

%O 1,3

%A _Stefano Spezia_, Feb 02 2022