login
Triangle read by rows: T(n,k) (n>=1, 1 <= k <= n) = number of n-element unlabeled rigid interval posets of height k.
2

%I #18 Nov 18 2021 11:27:33

%S 1,0,1,0,1,1,0,1,3,1,0,1,8,6,1,0,1,20,29,10,1,0,1,51,128,75,15,1,0,1,

%T 134,555,500,160,21,1,0,1,367,2427,3190,1480,301,28,1,0,1,1048,10864,

%U 20129,12835,3661,518,36,1,0,1,3119,50145,127912,108308,41041,7980,834,45,1,0,1,9655,239581,827053,907923,441553,111671,15828,1275,55,1

%N Triangle read by rows: T(n,k) (n>=1, 1 <= k <= n) = number of n-element unlabeled rigid interval posets of height k.

%H Soheir Mohamed Khamis, <a href="https://doi.org/10.1007/s11083-011-9213-5">Exact Counting of Unlabeled Rigid Interval Posets Regarding or Disregarding Height</a>, Order 29, pp. 443-461 (2012).

%e Triangle begins

%e 1

%e 0 1

%e 0 1 1

%e 0 1 3 1

%e 0 1 8 6 1

%e 0 1 20 29 10 1

%e 0 1 51 128 75 15 1

%e 0 1 134 555 500 160 21 1

%e 0 1 367 2427 3190 1480 301 28 1

%e 0 1 1048 10864 20129 12835 3661 518 36 1

%e 0 1 3119 50145 127912 108308 41041 7980 834 45 1

%e 0 1 9655 239581 827053 907923 441553 111671 15828 1275 55 1

%e 0 1 31024 1186941 5474614 7654921 4664814 1482110 26944 29175 1870 66 1

%e ...

%Y Row sums = A138265. Cf. A193387.

%K nonn,tabl

%O 1,9

%A _N. J. A. Sloane_, Aug 26 2011