A181279 Number of 3 X n binary matrices M with rows in strictly increasing order and rows of M*Mtranspose (mod 2) in strictly decreasing order.

0, 0, 9, 79, 766, 6060, 49928, 395024, 3170784, 25244608, 201926272, 1612664064, 12897654272, 103124642816, 824888150016, 6597998055424, 52781434593280, 422230539485184, 3377790630133760, 27021938497224704, 216174442832068608

Offset

1,3

Comments

Row 3 of A181274.

Links

R. H. Hardin, Table of n, a(n) for n=1..144

Formula

Empirical (for n>=3): 3*2^(3*n-7) + (18*n - 105 - 17*(-1)^n)*4^(n-4)/3 - (6*n - 19 - 3*(-1)^n)*2^(n-5)/3. - Vaclav Kotesovec, Nov 27 2012

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

G.f.: x^3*(9 - 47*x - 16*x^2 + 124*x^3 + 224*x^4 - 320*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..0......1..1..0
..0..1..1......1..0..0
..1..0..0......0..0..1

Crossrefs

Cf. A181274.

Sequence in context: A190979 A254598 A083411 * A173808 A348895 A293723

Adjacent sequences: A181276 A181277 A181278 * A181280 A181281 A181282

Keyword

nonn

Author

R. H. Hardin, Oct 10 2010

Status

approved