A181271 Number of 3 X n binary matrices M with rows in strictly increasing order and rows of M*Mtranspose (mod 2) in strictly increasing order.

0, 0, 6, 87, 730, 6236, 49400, 398032, 3162528, 25293504, 201794944, 1613449472, 12895556096, 103137221632, 824854591488, 6598199365632, 52780897705984, 422233760645120, 3377782040133632, 27021990036570112, 216174305392852992

Offset

1,3

Comments

Row 3 of A181266.

Links

R. H. Hardin, Table of n, a(n) for n=1..146

Formula

Empirical (for n>=3): 3*2^(3*n-7) + (18*n - 99 + 13*(-1)^n)*4^(n-4)/3 - (6*n - 1 + 3*(-1)^n)*2^(n-5)/3. - Vaclav Kotesovec, Nov 27 2012

Conjectures from Colin Barker, Mar 27 2018: (Start)

G.f.: x^3*(6 + 3*x - 272*x^2 + 444*x^3 + 832*x^4 - 960*x^5 - 512*x^6) / ((1 - 2*x)^2*(1 + 2*x)*(1 - 4*x)^2*(1 + 4*x)*(1 - 8*x)).

a(n) = 14*a(n-1) - 36*a(n-2) - 216*a(n-3) + 1056*a(n-4) - 384*a(n-5) - 3584*a(n-6) + 4096*a(n-7) for n>9.

(End)

Example

M and M*Mtranspose (mod 2) for 3 X 3:
..0..1..1......0..0..1
..1..0..0......0..1..1
..1..0..1......1..1..0

Crossrefs

Cf. A181266.

Sequence in context: A343636 A369624 A047786 * A249929 A289394 A113666

Adjacent sequences: A181268 A181269 A181270 * A181272 A181273 A181274

Keyword

nonn

Author

R. H. Hardin, Oct 10 2010

Status

approved