The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A331638 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A331638

Number of binary matrices with nonzero rows, a total of n ones and each column with the same number of ones and columns in nonincreasing lexicographic order.
(history; published version)

#9 by OEIS Server at Tue Oct 15 17:42:52 EDT 2024

LINKS

Andrew Howroyd, <a href="/A331638/b331638_1.txt">Table of n, a(n) for n = 1..200</a>

#8 by Alois P. Heinz at Tue Oct 15 17:42:52 EDT 2024

STATUS

proposed

approved

Discussion

Tue Oct 15

17:42

OEIS Server: Installed first b-file as b331638.txt.

#7 by Andrew Howroyd at Tue Oct 15 17:13:38 EDT 2024

STATUS

editing

proposed

#6 by Andrew Howroyd at Tue Oct 15 16:55:20 EDT 2024

LINKS

Andrew Howroyd, <a href="/A331638/b331638_1.txt">Table of n, a(n) for n = 1..200</a>

STATUS

approved

editing

#5 by Alois P. Heinz at Thu Jan 23 16:48:55 EST 2020

STATUS

proposed

approved

#4 by Andrew Howroyd at Thu Jan 23 16:03:47 EST 2020

STATUS

editing

proposed

#3 by Andrew Howroyd at Thu Jan 23 16:03:20 EST 2020

CROSSREFS

Cf. A330942, A331639.

#2 by Andrew Howroyd at Thu Jan 23 15:49:39 EST 2020

NAME

allocated for Andrew HowroydNumber of binary matrices with nonzero rows, a total of n ones and each column with the same number of ones and columns in nonincreasing lexicographic order.

DATA

1, 3, 5, 16, 17, 140, 65, 1395, 2969, 22176, 1025, 1050766, 4097, 13010328, 128268897, 637598438, 65537, 64864962683, 262145, 1676258452736, 28683380484257, 24908619669860, 4194305, 30567710172480050, 8756434134071649, 62128557507554504, 21271147396968151093

OFFSET

1,2

COMMENTS

The condition that the columns be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of columns.

FORMULA

a(n) = Sum_{d|n} A330942(n/d, d).

a(p) = 2^(p-1) + 1 for prime p.

CROSSREFS

Cf. A330942.

KEYWORD

allocated

nonn

AUTHOR

Andrew Howroyd, Jan 23 2020

STATUS

approved

editing

#1 by Andrew Howroyd at Thu Jan 23 12:24:34 EST 2020

NAME

allocated for Andrew Howroyd

KEYWORD

allocated

STATUS

approved