A224549 Number of (n+1) X 8 0..1 matrices with each 2 X 2 subblock idempotent.

216, 345, 472, 682, 943, 1323, 1858, 2652, 3845, 5681, 8544, 13062, 20247, 31739, 50190, 79892, 127789, 205117, 330056, 532022, 858611, 1386835, 2241302, 3623632, 5860053, 9478413, 15332788, 24805102, 40131355, 64929471, 105053374, 169974912

Offset

1,1

Comments

Column 7 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*(216 - 519*x + 172*x^2 + 303*x^3 - 202*x^4 + 15*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Aug 31 2018

Example

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

Crossrefs

Cf. A224550.

Sequence in context: A115430 A278976 A179419 * A339245 A327284 A376936

Adjacent sequences: A224546 A224547 A224548 * A224550 A224551 A224552

Keyword

nonn

Author

R. H. Hardin, Apr 10 2013

Status

approved