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 A221880 #13 Aug 15 2025 04:59:40 %S A221880 1,2,8,22,57,136,315,710,1577,3460,7527,16258,34917,74624,158819, %T A221880 336766,711777,1500028,3152991,6611834,13835357,28894072,60234843, %U A221880 125363062,260512857,540599156,1120345175,2318984050,4794555477,9902285680,20430920787,42114540398 %N A221880 Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with exactly 1 fixed point. %H A221880 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 A221880 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 %H A221880 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,-1,8,-4). %F A221880 a(n) = A221878(n,1). %F A221880 a(n) = A059570(n) + A221876(n,1) - n. %F A221880 G.f.: x*(1-3*x+5*x^2-3*x^3-3*x^4+x^5)/((1+x)*(1-3*x+2*x^2)^2). [_Bruno Berselli_, Mar 01 2013] %F A221880 a(n) = -n+(2^(n-1)*(21*n+34)-8*(-1)^n)/36 for n>1, a(1)=1. [_Bruno Berselli_, Mar 01 2013] %e A221880 a(3) = 8 because there are exactly 8 order-preserving or order-reversing full contraction mappings (of a 3-chain) with exactly 1 fixed point, namely: (111), (112), (222), (233), (333), (321), (322), (221). %Y A221880 Cf. A221876, A221877, A221878, A221879, A221881, A221882. %K A221880 nonn,easy %O A221880 1,2 %A A221880 _Abdullahi Umar_, Feb 28 2013 %E A221880 More terms from _Bruno Berselli_, Mar 01 2013