A051366 Number of 6-element families of an n-element set such that every 4 members of the family have a nonempty intersection.

0, 0, 0, 0, 112, 39761, 5318420, 506289623, 41378309308, 3133123494417, 227657567966500, 16152548751321851, 1129224692910819164, 78169242144478858373, 5373159786842137703140, 367368738925063893430959

Offset

0,5

References

V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).

Links

G. C. Greubel, Table of n, a(n) for n = 0..550

Formula

a(n) = (1/6!)*(64^n - 15*60^n + 60*58^n + 25*57^n - 240*56^n + 45*55^n + 705*54^n - 987*53^n - 351*52^n + 3040*51^n - 5445*50^n + 6105*49^n - 4939*48^n + 2997*47^n - 1365*46^n + 455*45^n - 105*44^n + 15*43^n - 42^n - 15*32^n + 75*30^n - 150*29^n + 150*28^n - 75*27^n + 15*26^n + 85*16^n - 85*15^n - 225*8^n + 225*7^n + 274*4^n - 274*3^n - 120*2^n + 120).

Mathematica

Table[1/6! (64^n - 15*60^n + 60*58^n + 25*57^n - 240*56^n + 45*55^n + 705*54^n - 987*53^n - 351*52^n + 3040*51^n - 5445*50^n + 6105*49^n - 4939*48^n + 2997*47^n - 1365*46^n + 455*45^n - 105*44^n + 15*43^n - 42^n - 15*32^n + 75*30^n - 150*29^n + 150*28^n - 75*27^n + 15*26^n + 85*16^n - 85*15^n - 225*8^n + 225*7^n + 274*4^n - 274*3^n - 120*2^n + 120), {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)

Crossrefs

Cf. A036239, A051180, A051181, A051182, A051183, A051184, A051185.

Sequence in context: A206310 A331670 A063409 * A051363 A362963 A304394

Adjacent sequences: A051363 A051364 A051365 * A051367 A051368 A051369

Keyword

nonn

Author

Vladeta Jovovic, Goran Kilibarda

Status

approved