A153836 a(n) = 2^(n^2) - 2^(n^2 - n + 1) for n >= 1; a(0) = 0.

0, 0, 8, 384, 57344, 31457280, 66571993088, 554153860399104, 18302628885633695744, 2408406906263519058984960, 1265174720149658640946904956928, 2655859843140564331993348872396079104, 22289856162789153110704890285210544923213824

Offset

0,3

Comments

Number of binary relations on an n-element set that are neither reflexive nor irreflexive. Note that "irreflexive" = "antireflexive".

The empty relation, unlike all others, is (trivially) both reflexive and irreflexive.

Links

G. C. Greubel, Table of n, a(n) for n = 0..50

Formula

a(n) = 2^(n^2) - 2^(n^2 -n +1) = A002416(n) - 2*A053763(n) for n >= 1; a(0) = 0.

Mathematica

Join[{0}, Table[2^(n^2) - 2^(n^2 - n + 1), {n, 1, 25}]] (* G. C. Greubel, Aug 30 2016 *)

Prog

(PARI) a(n) = if(n<=0, 0, 2^(n^2)-2^(n^2-n+1))
(Magma) [0] cat [2^(n^2) - 2^(n^2 -n +1): n in [1..15]]; // Vincenzo Librandi, Aug 31 2016

Crossrefs

Cf. A002416, A053763.

Sequence in context: A162445 A067624 A096204 * A151941 A085806 A042115

Adjacent sequences: A153833 A153834 A153835 * A153837 A153838 A153839

Keyword

nonn

Author

Rick L. Shepherd, Jan 02 2009

Status

approved