A184052 The number of order-decreasing partial isometries (of an n-chain)

1, 2, 5, 13, 30, 66, 137, 279, 556, 1104, 2179, 4309, 8518, 16886, 33509, 66643, 132672, 264492, 527639, 1053441, 2104042, 4204242, 8402617, 16797343, 33582724, 67149416, 134274635, 268516909, 536985102, 1073905134, 2147712461, 4295294379, 8590392712, 17180523876, 34360655167, 68720786713

Offset

0,2

Links

Table of n, a(n) for n=0..35.

R. Kehinde, S. O. Makanjuola and A. Umar, On the semigroup of order-decreasing partial isometries of a finite chain, arXiv:1101.2558

Index entries for linear recurrences with constant coefficients, signature (5,-7,-3,16,-14,4).

Formula

a(n) = 3*a(n-1)-2*a(n-2)-2^floor(n/2)+n+1.

G.f.: ( -1+3*x-2*x^2-5*x^3-4*x^5+10*x^4 ) / ( (2*x-1)*(2*x^2-1)*(x-1)^3 ). - R. J. Mathar, Jul 03 2011

Example

a(2) = 5 because there are exactly 5 order-decreasing partial isometries (on a 2-chain) namely: empty map; 1-->1; 2-->1; 2-->2; (1,2)-->(1,2) - the mappings are coordinate-wise

Crossrefs

It is the row sum of A184051

Sequence in context: A290198 A282153 A054127 * A295057 A309535 A018012

Adjacent sequences: A184049 A184050 A184051 * A184053 A184054 A184055

Keyword

nonn

Author

Abdullahi Umar, Jan 12 2011

Status

approved