OFFSET
0,4
LINKS
R. Kehinde, A. Umar, On the semigroup of partial isometries of a finite chain, arXiv:1101.0049
EXAMPLE
T (4,2) = 6 because there are exactly 6 partial isometries (on a 4-chain) of fix 2, namely: (1,2)-->(1,2); (2,3)-->(2,3); (3,4)-->(3,4); (1,3)-->(1,3); (2,4)-->(2,4); (1,4)-->(1,4) - the mappings are coordinate-wise.
...1.
...1....1.
...4....2....1.
..12....6....3....1.
..38...10....6....4....1.
..90...26...10...10....5....1.
.220...42...15...20...15....6....1.
.460..106...21...35...35...21....7....1.
1018..170...28...56...70...56...28....8....1.
2022..426...36...84..126..126...84...36....9....1.
4304..682...45..120..210..252..210..120...45...10....1.
MAPLE
A183159 := proc(n) nh := floor(n/2) ; if type(n, 'even') then 13*4^nh-12*nh^2-18*nh-10; else 25*4^nh-12*nh^2-30*nh-22; end if; %/3 ; end proc:
A061547 := proc(n) 3*2^n/8 +(-2)^n/24 - 2/3; end proc:
A183158 := proc(n, k) if k = 0 then A183159(n) ; elif k = 1 then A061547(n+1) ; else binomial(n, k) ; end if; end proc: # R. J. Mathar, Jan 06 2011
MATHEMATICA
T[n_, 0] := (51*2^n + (-2)^n - 40)/12 - n*(n + 3);
T[n_, 1] := (9*2^n + (-1)^(n+1)*2^n - 8)/12;
T[n_, k_] := Binomial[n, k];
Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 22 2017 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Abdullahi Umar, Dec 28 2010
STATUS
approved