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A361954
Triangle read by rows: T(n,k) is the number of unlabeled connected weakly graded (ranked) posets with n elements and rank k.
4
1, 0, 1, 0, 2, 1, 0, 4, 5, 1, 0, 10, 23, 8, 1, 0, 27, 107, 56, 11, 1, 0, 88, 557, 388, 98, 14, 1, 0, 328, 3271, 2888, 839, 149, 17, 1, 0, 1460, 22424, 23900, 7512, 1470, 209, 20, 1, 0, 7799, 183273, 226807, 73405, 14715, 2308, 278, 23, 1
OFFSET
1,5
COMMENTS
Here weakly graded means that there exists a rank function rk from the poset to the integers such that whenever v covers w in the poset, we have rk(v) = rk(w) + 1.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..820 (rows 1..40)
Wikipedia, Graded poset.
EXAMPLE
Triangle begins:
1;
0, 1;
0, 2, 1;
0, 4, 5, 1;
0, 10, 23, 8, 1;
0, 27, 107, 56, 11, 1;
0, 88, 557, 388, 98, 14, 1;
0, 328, 3271, 2888, 839, 149, 17, 1;
...
PROG
(PARI) \\ See PARI link in A361953 for program code.
{ my(A=A361954tabl(8)); for(i=1, #A, print(A[i, 1..i])) }
CROSSREFS
Column k=2 is A007776.
Row sums are A361955.
Cf. A342500, A361953 (not necessarily connected).
Sequence in context: A073592 A164994 A269952 * A342500 A247268 A266867
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Mar 31 2023
STATUS
approved