A319366 Number of 6 X n binary matrices such that any 2 rows have a common 1.

1, 127, 14197, 1527655, 154708741, 14581420567, 1282928605477, 106281575400295, 8370106554738181, 632240233746846007, 46159332156459328357, 3278558540783856976135, 227767526682511220042821, 15545657368091391819871447, 1046175606578621216182684837

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Mathematics Stack Exchange, An interesting combinatorics problem

Quora, How many ways are there to set N people into M groups so that every two groups have at least one common member?

Formula

a(n) = 64^n - 15*48^n + 60*40^n - 15*36^n + 30*34^n - 6*33^n - 200*32^n - 180*30^n + 585*28^n + 45*27^n + 60*26^n + 150*25^n - 660*24^n - 360*23^n + 168*22^n - 585*21^n + 1245*20^n + 1665*19^n - 1965*18^n - 2100*17^n + 2170*16^n + 1325*15^n - 1770*14^n - 420*13^n + 1533*12^n - 1105*11^n + 435*10^n - 105*9^n + 15*8^n - 7^n (proved in the Quora answer).

Crossrefs

Cf. A051587, A051588, A051589.

Sequence in context: A022189 A121618 A069382 * A221979 A058322 A252483

Adjacent sequences: A319363 A319364 A319365 * A319367 A319368 A319369

Keyword

nonn

Author

T. V. Raziman, Sep 17 2018

Status

approved