A221880 Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with exactly 1 fixed point.

1, 2, 8, 22, 57, 136, 315, 710, 1577, 3460, 7527, 16258, 34917, 74624, 158819, 336766, 711777, 1500028, 3152991, 6611834, 13835357, 28894072, 60234843, 125363062, 260512857, 540599156, 1120345175, 2318984050, 4794555477, 9902285680, 20430920787, 42114540398

Offset

1,2

References

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).

Links

Table of n, a(n) for n=1..32.

Index entries for linear recurrences with constant coefficients, signature (5,-7,-1,8,-4).

Formula

a(n) = A221878(n,1).

a(n) = A059570(n) + A221876(n,1) - n.

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]

a(n) = -n+(2^(n-1)*(21*n+34)-8*(-1)^n)/36 for n>1, a(1)=1. [Bruno Berselli, Mar 01 2013]

Example

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).

Crossrefs

Cf. A221876, A221877, A221878, A221879, A221881, A221882.

Sequence in context: A006732 A005803 A145654 * A295141 A074352 A301555

Adjacent sequences: A221877 A221878 A221879 * A221881 A221882 A221883

Keyword

nonn,easy

Author

Abdullahi Umar, Feb 28 2013

Extensions

More terms from Bruno Berselli, Mar 01 2013

Status

approved