A224561 Number of (n+3) X 4 0..1 matrices with each 4 X 4 subblock idempotent.

452, 370, 512, 739, 990, 1345, 1852, 2659, 3846, 5589, 8064, 11675, 16954, 24757, 36196, 52963, 77458, 113341, 165916, 243035, 356062, 521713, 764408, 1120079, 1641326, 2405317, 3525004, 5165987, 7570886, 11095421, 16260864, 23831255

Offset

1,1

Comments

Column 1 of A224568.

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) + a(n-3) + a(n-4) - 2*a(n-5) + 2*a(n-6) - 2*a(n-7) + a(n-8) for n>10.

Empirical g.f.: x*(452 - 986*x + 758*x^2 - 139*x^3 - 513*x^4 + 614*x^5 - 628*x^6 + 597*x^7 - 168*x^8 - 13*x^9) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 - x - x^3)). - Colin Barker, Sep 01 2018

Example

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

Crossrefs

Cf. A224568.

Sequence in context: A128922 A224560 A224568 * A116308 A183636 A222823

Adjacent sequences: A224558 A224559 A224560 * A224562 A224563 A224564

Keyword

nonn

Author

R. H. Hardin, Apr 10 2013

Status

approved