A110730 - OEIS

%I #28 Jun 13 2021 22:16:48

%S 1,1,1,2,1,1,1,2,2,3,1,1,1,1,2,2,2,3,3,4,1,1,1,1,1,2,2,2,2,3,3,3,4,4,

%T 5,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4,4,4,5,5,6,1,1,1,1,1,1,1,2,2,2,2,2,

%U 2,3,3,3,3,3,4,4,4,4,5,5,5,6,6,7,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3

%N Irregular triangle read by rows in which row n lists n 1's followed by (n-1) 2's followed by (n-3) 3's ... followed by 1 n.

%C From _Omar E. Pol_, May 08 2021: (Start)

%C Row n has length A000217(n).

%C Row sums give A000292, n >= 1.

%C Row n lists the terms of the n-th row A333516 in nondecreasing order.

%C (End)

%e From _Omar E. Pol_, May 08 2021: (Start)

%e Triangle begins:

%e   1;

%e   1, 1, 2;

%e   1, 1, 1, 2, 2, 3;

%e   1, 1, 1, 1, 2, 2, 2, 3, 3, 4;

%e   1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5;

%e   1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6;

%e   ...

%e (End)

%t Flatten@Array[Table[Table[k,#-k+1],{k,#}]&,10] (* _Giorgos Kalogeropoulos_, Jun 08 2021 *)

%Y Cf. A004736.

%Y Cf. A000217, A000292, A333516, A345116 (mirror).

%K base,easy,tabf,nonn

%O 1,4

%A _Amarnath Murthy_, Aug 09 2005

%E Name clarified by _Omar E. Pol_, Jun 08 2021