

A183159


The number of partial isometries (of an nchain) of fix zero (fix of alpha = 0)). Equivalently, the number of partial derangement isometries (of an nchain).


3



1, 1, 4, 12, 38, 90, 220, 460, 1018, 2022, 4304, 8376, 17566, 33922, 70756, 136260, 283682, 545790, 1135576, 2184112, 4543366, 8737626, 18174764, 34951932, 72700618, 139809430, 290804320, 559239720, 1163219438
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OFFSET

0,3


LINKS

Table of n, a(n) for n=0..28.
R. Kehinde and A. Umar, On the semigroup of partial isometries of a finite chain, arXiv:1101.2558
Index entries for linear recurrences with constant coefficients, signature (3,1,11,12,4).


FORMULA

a(2n) = (13*4^n12*n^218*n10)/3, n>=0.
a(2n+1) = (25*4^n12*n^230*n22)/3, n>=0.
a(n) = A183158(n,0).
G.f.: ( 12*x3*x^4+10*x^3 ) / ( (2*x1)*(2*x+1)*(x1)^3 ).  Joerg Arndt, Dec 30 2010
a(n) = (51*2^n+(2)^n40)/12n*(n+3).  JeanFrançois Alcover, Nov 22 2017


EXAMPLE

a(2) = 4 because there are exactly 4 partial derangement isometries (on a 2chain) , namely: empty map; 1>2; 2>1; (1,2)>(2,1). a(3) = 12 because there are exactly 12 partial isometries (on a 3chain) namely: empty map; 1>2; 1>3; 2>1; 2>3; 3>1; 3>2; (1,2)>(2,1); (1,2)>(2,3); (2,3)>(1,2); (2,3)>(3,2); (1,3)>(3,1)  the mappings are coordinatewise.


MAPLE

A183159 := proc(n) nh := floor(n/2) ; if type(n, 'even') then 13*4^nh12*nh^218*nh10; else 25*4^nh12*nh^230*nh22; end if; %/3 ; end proc:
seq(A183159(n), n=0..50) ; # R. J. Mathar, Jan 06 2011


MATHEMATICA

LinearRecurrence[{3, 1, 11, 12, 4}, {1, 1, 4, 12, 38}, 30] (* Harvey P. Dale, Dec 06 2015 *)
a[n_] := (51*2^n+(2)^n40)/12n*(n+3); Array[a, 29, 0] (* JeanFrançois Alcover, Nov 22 2017 *)


CROSSREFS

Sequence in context: A149323 A024590 A189499 * A289809 A014345 A006192
Adjacent sequences: A183156 A183157 A183158 * A183160 A183161 A183162


KEYWORD

nonn


AUTHOR

Abdullahi Umar, Dec 28 2010


STATUS

approved



