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 A221882 #31 Aug 18 2025 06:27:42
%S A221882 1,4,13,36,91,218,505,1144,2551,5622,12277,26612,57331,122866,262129,
%T A221882 557040,1179631,2490350,5242861,11010028,23068651,48234474,100663273,
%U A221882 209715176,436207591,905969638,1879048165,3892314084,8053063651,16642998242,34359738337
%N A221882 Number of order-preserving or order-reversing full contraction mappings of an n-chain.
%C A221882 a(n) is the order of the semigroup (monoid) of order-preserving or order-reversing full contraction mappings (of an n-chain).
%H A221882 Paolo Xausa, <a href="/A221882/b221882.txt">Table of n, a(n) for n = 1..3000</a>
%H A221882 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 A221882 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 A221882 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4).
%F A221882 a(n) = (n+1)*2^(n-1) - n.
%F A221882 a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4).
%F A221882 a(n) = Sum_{k=1..n} A221877(n,k) = Sum_{k=0..n-1} A221878(n,k) = Sum_{k=1..n} A221881(n,k). [Edited by _Paolo Xausa_, Aug 18 2025]
%F A221882 G.f.: x*(1-2*x+2*x^2-2*x^3)/(1-3*x+2*x^2)^2. [_Bruno Berselli_, Mar 01 2013]
%e A221882 a(3) = 13 because there are exactly 13 order-preserving or order-reversing full contraction mappings of a 3-chain, namely: (111), (112), (211), (122), (221), (123), (321), (222), (223), (233), (322), (332), (333).
%t A221882 A221882[n_] := (n + 1)*2^(n - 1) - n; Array[A221882, 50] (* or *)
%t A221882 LinearRecurrence[{6, -13, 12, -4}, {1, 4, 13, 36}, 50] (* _Paolo Xausa_, Aug 18 2025 *)
%o A221882 (PARI) a(n)=(n+1)<<(n-1)-n; \\ _Charles R Greathouse IV_, Feb 28 2013
%Y A221882 Cf. A045992, A221876, A221877, A221878, A221880, A221881.
%K A221882 nonn,easy
%O A221882 1,2
%A A221882 _Abdullahi Umar_, Feb 28 2013
%E A221882 More terms from _Joerg Arndt_, Mar 01 2013