A224563 Number of (n+3) X 6 0..1 matrices with each 4 X 4 subblock idempotent.

512, 428, 514, 629, 728, 929, 1232, 1627, 2095, 2739, 3658, 4945, 6670, 9010, 12237, 16720, 22894, 31375, 43047, 59167, 81423, 112123, 154455, 212868, 293495, 404781, 558355, 770299, 1062824, 1466590, 2023882, 2793071, 3854735, 5320116, 7342737

Offset

1,1

Comments

Column 3 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*(512 - 1108*x + 254*x^2 + 967*x^3 - 1323*x^4 + 855*x^5 + 387*x^6 - 753*x^7 + 167*x^8 + 40*x^9) / ((1 - x)^3*(1 + x)*(1 - x - x^4)). - Colin Barker, Sep 01 2018

Example

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

Crossrefs

Cf. A224568.

Sequence in context: A190025 A077743 A111447 * A217849 A326113 A045003

Adjacent sequences: A224560 A224561 A224562 * A224564 A224565 A224566

Keyword

nonn

Author

R. H. Hardin, Apr 10 2013

Status

approved