|
%I #10 Apr 01 2023 14:27:39
%S 1,1,0,1,1,0,1,2,1,0,1,3,4,1,0,1,4,8,8,1,0,1,5,13,21,17,1,0,1,6,19,40,
%T 58,38,1,0,1,7,26,66,126,172,94,1,0,1,8,34,100,228,420,569,258,1,0,1,
%U 9,43,143,373,816,1537,2148,815,1,0,1,10,53,196,571,1412,3140,6342,9538,3038,1,0
%N Array read by antidiagonals: T(n,k) is the number of unlabeled posets with n elements together with a function rk mapping each element to a rank between 1 and k such that whenever v covers w in the poset then rk(v) = rk(w) + 1.
%C A poset is counted once for each admissible ranking function. This is an intermediate step in the computation of A361953 where each graded poset is counted exactly once.
%H Andrew Howroyd, <a href="/A361952/b361952.txt">Table of n, a(n) for n = 0..860</a> (first 41 antidiagonals).
%e Array begins:
%e ============================================
%e n/k| 0 1 2 3 4 5 6 7 ...
%e ---+----------------------------------------
%e 0 | 1 1 1 1 1 1 1 1 ...
%e 1 | 0 1 2 3 4 5 6 7 ...
%e 2 | 0 1 4 8 13 19 26 34 ...
%e 3 | 0 1 8 21 40 66 100 143 ...
%e 4 | 0 1 17 58 126 228 373 571 ...
%e 5 | 0 1 38 172 420 816 1412 2272 ...
%e 6 | 0 1 94 569 1537 3140 5631 9351 ...
%e 7 | 0 1 258 2148 6342 13383 24410 41097 ...
%e ...
%o (PARI) \\ See Links in A361953 for program.
%o { my(A=A361952tabl(7)); for(i=1, #A, print(A[i,])) }
%Y Columns k=0..2 are A000007, A000012, A049312.
%Y Rows n=0..4 are A000012, A000027, A034856, A137742.
%Y The labeled version is A361950.
%Y Cf. A361953.
%K nonn,tabl
%O 0,8
%A _Andrew Howroyd_, Mar 31 2023
|
