A224567 Number of (n+3) X 10 0..1 matrices with each 4 X 4 subblock idempotent.

1852, 1044, 1232, 1433, 1614, 1997, 2526, 3175, 3917, 4951, 6416, 8429, 11076, 14646, 19563, 26372, 35700, 48467, 66013, 90227, 123621, 169631, 233029, 320480, 441157, 607673, 837409, 1154415, 1591910, 2195730, 3029088, 4179251, 5766701, 7957760

Offset

1,1

Comments

Column 7 of A224568.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 4*a(n-4) - 3*a(n-5) + 2*a(n-7) -a(n-8) for n>10.

Empirical g.f.: x*(1852 - 4512*x + 1804*x^2 + 3529*x^3 - 5541*x^4 + 3865*x^5 + 833*x^6 - 2921*x^7 + 1045*x^8 + 36*x^9) / ((1 - x)^3*(1 + x)*(1 - x - x^4)). Colin Barker, Sep 01 2018

Example

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

Crossrefs

Cf. A224568.

Sequence in context: A031674 A031541 A031721 * A303272 A128289 A023044

Adjacent sequences: A224564 A224565 A224566 * A224568 A224569 A224570

Keyword

nonn

Author

R. H. Hardin, Apr 10 2013

Status

approved