A224545 Number of (n+1) X 4 0..1 matrices with each 2 X 2 subblock idempotent.

28, 52, 78, 125, 193, 302, 472, 743, 1175, 1868, 2982, 4777, 7673, 12350, 19908, 32127, 51887, 83848, 135550, 219193, 354517, 573462, 927708, 1500875, 2428263, 3928792, 6356682, 10285073, 16641325, 26925938, 43566772, 70492187, 114058403

Offset

1,1

Comments

Column 3 of A224550.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5) for n>6.

Empirical g.f.: x*(28 - 60*x + 10*x^2 + 45*x^3 - 25*x^4 + x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Aug 30 2018

Example

Some solutions for n=3:
..1..0..0..0....1..1..0..0....1..1..0..1....1..0..0..0....1..0..1..0
..1..0..0..0....0..0..0..0....0..0..0..1....1..0..0..0....1..0..1..0
..0..0..0..0....0..0..0..0....0..0..0..1....0..0..0..0....1..0..1..0
..0..0..0..1....1..1..1..1....0..0..0..1....0..0..1..1....1..0..1..0

Crossrefs

Cf. A224550.

Sequence in context: A291855 A181792 A181793 * A216303 A261105 A043134

Adjacent sequences: A224542 A224543 A224544 * A224546 A224547 A224548

Keyword

nonn

Author

R. H. Hardin, Apr 10 2013

Status

approved