

A183154


T(n,k) is the number of orderpreserving partial isometries (of an nchain) of fixed k (fix of alpha is the number of fixed points of alpha)


3



1, 1, 1, 3, 2, 1, 9, 3, 3, 1, 23, 4, 6, 4, 1, 53, 5, 10, 10, 5, 1, 115, 6, 15, 20, 15, 6, 1, 241, 7, 21, 35, 35, 21, 7, 1, 495, 8, 28, 56, 70, 56, 28, 8, 1, 1005, 9, 36, 84, 126, 126, 84, 36, 9, 1, 2027, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1
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OFFSET

0,4


LINKS



FORMULA

T(n,0) = A183155(n) and T(n,k) = binomial(n,k) if k > 0.


EXAMPLE

T (4,2) = 6 because there are exactly 6 orderpreserving partial isometries (on a 4chain) 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 coordinatewise.
Triangle starts as:
1;
1, 1;
3, 2, 1;
9, 3, 3, 1;
23, 4, 6, 4, 1;
53, 5, 10, 10, 5, 1;
115, 6, 15, 20, 15, 6, 1;


MAPLE

A183155 := proc(n) 2^(n+1)2*n1 ; end proc:


MATHEMATICA

T[n_, k_] := If[k == 0, 2^(n + 1)  2n  1, Binomial[n, k]];


PROG

(PARI) A183155(n)=2^(n+1)  (2*n+1);
T(n, k)=if(k==0, A183155(n), binomial(n, k));
for(n=0, 17, for(k=0, n, print1(T(n, k), ", ")); print()) \\ Joerg Arndt, Dec 30 2010


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



