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A221880 Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with exactly 1 fixed point. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 21 16:04 EST 2019. Contains 329371 sequences. (Running on oeis4.)