This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A221881 #17 Aug 15 2025 05:00:01
%S A221881 1,1,3,1,5,7,1,7,13,15,1,9,21,29,31,1,11,31,51,61,63,1,13,43,83,113,
%T A221881 125,127,1,15,57,127,197,239,253,255,1,17,73,185,325,437,493,509,511,
%U A221881 1,19,91,259,511,763,931,1003,1021,1023
%N A221881 Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with (right) waist exactly k.
%C A221881 Row sums are A221882.
%H A221881 A. D. Adeshola, V. Maltcev and A. Umar, <a href="http://arxiv.org/abs/1303.7428">Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain</a>, arXiv:1303.7428 [math.CO], 2013.
%H A221881 A. D. Adeshola, A. Umar, <a href="https://combinatorialpress.com/jcmcc/vol106/">Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain</a>, JMCC 106 (2017) 37-49
%F A221881 T(n,k) = 2*Sum_{p=1..k} C(n-1,p-1) - 1 for k >=1.
%e A221881 T(5,2) = 9 because there are exactly 9 order-preserving or order-reversing full contraction mappings (of a 5-chain) with (right) waist exactly 2, namely: (11112), (11122), (11222), (12222), (21111), (22111), (22211), (22221), (22222).
%Y A221881 Cf. A221876, A221877, A221878, A221879, A221880, A221882.
%K A221881 nonn,tabl
%O A221881 1,3
%A A221881 _Abdullahi Umar_, Feb 28 2013