A224562 Number of (n+3) X 5 0..1 matrices with each 4 X 4 subblock idempotent.

370, 340, 428, 517, 611, 775, 1044, 1383, 1808, 2373, 3190, 4323, 5868, 7946, 10825, 14809, 20317, 27872, 38285, 52646, 72495, 99863, 137615, 189693, 261595, 360821, 497771, 686759, 947616, 1307656, 1804613, 2490510, 3437232, 4743946, 6547576

Offset

1,1

Comments

Column 2 of A224568.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-5) + a(n-6) - 2*a(n-7) + 2*a(n-8) + a(n-11) - a(n-12) for n>15.

Empirical g.f.: x*(370 - 400*x + 118*x^2 - 369*x^3 - 335*x^4 + 382*x^5 - 102*x^6 + 715*x^7 - 143*x^8 - 23*x^9 - 14*x^10 - 361*x^11 + 119*x^12 + 26*x^13 + 5*x^14) / ((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x + x^2)*(1 - x - x^4)). - Colin Barker, Sep 01 2018

Example

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

Crossrefs

Cf. A224568.

Sequence in context: A255202 A255194 A108772 * A276413 A161020 A102618

Adjacent sequences: A224559 A224560 A224561 * A224563 A224564 A224565

Keyword

nonn

Author

R. H. Hardin, Apr 10 2013

Status

approved