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URL: https://oeis.org/A184052

⇱ A184052 - OEIS

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A184052
The number of order-decreasing partial isometries (of an n-chain).
1
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
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
KEYWORD
nonn
AUTHOR
Abdullahi Umar, Jan 12 2011
STATUS
approved