A224552 Number of (n+2) X 3 0..1 matrices with each 3 X 3 subblock idempotent.

50, 70, 113, 172, 263, 418, 669, 1064, 1699, 2734, 4409, 7108, 11471, 18538, 29973, 48464, 78379, 126790, 205121, 331852, 536903, 868690, 1405533, 2274152, 3679603, 5953678, 9633209, 15586804, 25219919, 40806634, 66026469, 106833008, 172859371

Offset

1,1

Comments

Column 1 of A224559.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - a(n-4) - a(n-5) + a(n-6) for n>7.

Empirical g.f.: x*(50 - 80*x + 53*x^2 - 57*x^3 - 4*x^4 + 39*x^5 - 7*x^6) / ((1 - x)^2*(1 + x^2)*(1 - x - x^2)). - Colin Barker, Aug 31 2018

Example

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

Crossrefs

Cf. A224559.

Sequence in context: A102803 A224559 A272607 * A039473 A309123 A146170

Adjacent sequences: A224549 A224550 A224551 * A224553 A224554 A224555

Keyword

nonn

Author

R. H. Hardin, Apr 10 2013

Status

approved