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 A221878 #23 Aug 15 2025 04:59:08 %S A221878 1,0,1,1,2,1,2,8,2,1,6,22,5,2,1,14,57,12,5,2,1,34,136,28,12,5,2,1,78, %T A221878 315,64,28,12,5,2,1,178,710,144,64,28,12,5,2,1,398,1577,320,144,64,28, %U A221878 12,5,2,1,882,3460,704,320,144,64,28,12,5,2,1 %N A221878 Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with exactly k fixed points. %C A221878 Its row sum is A221882. %H A221878 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 A221878 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 A221878 T(n,0) = T(n-1,1), T(n,1) = A059570(n) + A221876(n,1) - n and T(n,k) = A221876 if k > 1. %e A221878 T (4,0) = 6 because there are exactly 6 order-preserving or order-reversing full contraction mappings (of a 4-chain) with no fixed point, namely: (2111), (3321), (3322), (4321), (4322), (4443). %e A221878 Triangle: %e A221878 1, %e A221878 0, 1, %e A221878 1, 2, 1, %e A221878 2, 8, 2, 1, %e A221878 6, 22, 5, 2, 1, %e A221878 14, 57, 12, 5, 2, 1, %e A221878 34, 136, 28, 12, 5, 2, 1, %e A221878 78, 315, 64, 28, 12, 5, 2, 1, %e A221878 178, 710, 144, 64, 28, 12, 5, 2, 1, %e A221878 398, 1577, 320, 144, 64, 28, 12, 5, 2, 1, %e A221878 882, 3460, 704, 320, 144, 64, 28, 12, 5, 2, 1 %Y A221878 Cf. A221876, A221877, A221879, A221880, A221881, A221882. %K A221878 nonn,tabl %O A221878 1,5 %A A221878 _Abdullahi Umar_, Feb 28 2013