A394449 Number of symmetric relations on an n-set that are neither reflexive nor transitive.

0, 0, 3, 46, 923, 31593, 2063710, 266335041, 68451024273, 35115652517268, 35993612646312541, 73750947497815707469, 302157667927362432039240, 2475577847115856892341317019, 40562343327224770087343512264361, 1329187430965708569562959156680588942

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = A006125(n+1) - A006125(n) - A000110(n+1) + A000110(n).

Example

On a 2-set {1,2}, there are exactly 3 such relations. Such relations on {1,2} are {(1,2),(2,1)}, {(1,1),(1,2),(2,1)}, {(2,2),(1,2),(2,1)}. So, a(2)=3.

Crossrefs

Cf. A006125, A000110, A005493, A202534, A394620, A006905, A000798, A053763.

Sequence in context: A231789 A377664 A386889 * A119401 A124135 A307292

Adjacent sequences: A394446 A394447 A394448 * A394450 A394451 A394452

Keyword

nonn

Author

Firdous Ahmad Mala, Apr 29 2026

Status

approved