A224547 Number of (n+1) X 6 0..1 matrices with each 2 X 2 subblock idempotent.

80, 137, 193, 294, 428, 635, 943, 1420, 2162, 3333, 5193, 8166, 12936, 20611, 32983, 52952, 85210, 137349, 221653, 357998, 578544, 935327, 1512543, 2446424, 3957398, 6402125, 10357693, 16757850, 27113432, 43869023, 70980043, 114846496

Offset

1,1

Comments

Column 5 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*(80 - 183*x + 45*x^2 + 127*x^3 - 80*x^4 + 6*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Aug 30 2018

Example

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

Crossrefs

Cf. A224550.

Sequence in context: A365867 A349307 A349308 * A204648 A202447 A202440

Adjacent sequences: A224544 A224545 A224546 * A224548 A224549 A224550

Keyword

nonn

Author

R. H. Hardin, Apr 10 2013

Status

approved