%I #20 Jun 13 2015 00:54:37
%S 1,4,13,36,91,218,505,1144,2551,5622,12277,26612,57331,122866,262129,
%T 557040,1179631,2490350,5242861,11010028,23068651,48234474,100663273,
%U 209715176,436207591,905969638,1879048165,3892314084,8053063651,16642998242,34359738337
%N Number of order-preserving or order-reversing full contraction mappings of an n-chain.
%C a(n) = Sum A221877(n,k) = Sum A221878(n,k) = Sum A221881(n,k).
%C a(n) is also the order of the semigroup (monoid) of order-preserving or order-reversing full contraction mappings (of an n-chain).
%D A. D. Adeshola, V. Maltcev, and A. Umar, Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain, (submitted 2013).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4).
%F a(n) = (n+1)*2^(n-1) - n.
%F a(n) = +6*a(n-1) -13*a(n-2) +12*a(n-3) -4*a(n-4).
%F 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 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).
%o (PARI) a(n)=(n+1)<<(n-1)-n; \\ _Charles R Greathouse IV_, Feb 28 2013
%Y Cf. A045992, A221876, A221877, A221878, A221880, A221881.
%K nonn,easy
%O 1,2
%A _Abdullahi Umar_, Feb 28 2013
%E More terms from _Joerg Arndt_, Mar 01 2013