A331655 Number of binary matrices with n distinct columns and any number of distinct nonzero rows with 4 ones in every column and rows in decreasing lexicographic order.

1, 0, 0, 1, 272, 64453, 23553340, 13241130441, 11008118941631, 13027230343637042, 21234181599255320655, 46357847997267210103060, 132373322228662190671151849, 484443861947038578745971380703, 2232754658868099948336222687731941, 12763566506391999019612414249332466653

Offset

0,5

Comments

The condition that the rows be in decreasing order is equivalent to considering nonequivalent matrices with distinct rows up to permutation of rows.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k)*A188446(k).

Example

The a(3) = 1 matrix is:
  [1 1 1]
  [1 1 0]
  [1 0 1]
  [1 0 0]
  [0 1 1]
  [0 1 0]
  [0 0 1]

Crossrefs

Row n=4 of A331039.

Cf. A188446.

Sequence in context: A280044 A162009 A283789 * A225833 A198289 A198595

Adjacent sequences: A331652 A331653 A331654 * A331656 A331657 A331658

Keyword

nonn

Author

Andrew Howroyd, Jan 24 2020

Status

approved