A224599 Number of (n+2) X 3 0..2 matrices with each 3 X 3 subblock idempotent.

122, 178, 297, 416, 628, 1045, 1694, 2668, 4265, 6922, 11196, 18035, 29122, 47134, 76253, 123292, 199424, 322681, 522090, 844664, 1366621, 2211238, 3577832, 5788951, 9366638, 15155530, 24522129, 39677528, 64199500, 103876957, 168076406

Offset

1,1

Comments

Column 1 of A224606.

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*(122 - 188*x + 129*x^2 - 185*x^3 + 37*x^4 + 115*x^5 - 36*x^6) / ((1 - x)^2*(1 + x^2)*(1 - x - x^2)). - Colin Barker, Sep 01 2018

Example

Some solutions for n=3:
..1..1..0....1..0..1....0..1..0....0..0..0....1..0..0....1..0..0....0..0..1
..0..0..0....0..0..0....0..1..0....0..0..0....0..0..0....0..0..0....0..0..1
..0..0..0....0..0..0....0..1..0....0..0..0....0..0..0....0..1..1....0..0..1
..1..0..1....0..0..0....0..1..0....2..1..1....2..1..1....0..0..0....0..0..1
..1..0..1....2..1..1....0..2..0....0..0..0....0..0..0....0..1..1....0..0..1

Crossrefs

Cf. A224606.

Sequence in context: A280733 A309760 A224606 * A207147 A222578 A105983

Adjacent sequences: A224596 A224597 A224598 * A224600 A224601 A224602

Keyword

nonn

Author

R. H. Hardin, Apr 11 2013

Status

approved