A224546 Number of (n+1) X 5 0..1 matrices with each 2 X 2 subblock idempotent.

48, 86, 125, 196, 294, 448, 682, 1049, 1626, 2543, 4007, 6355, 10131, 16216, 26035, 41894, 67524, 108962, 175976, 284371, 459720, 743401, 1202365, 1944941, 3146409, 5090378, 8235737, 13324984, 21559506, 34883188, 56441302, 91323005, 147762726

Offset

1,1

Comments

Column 4 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*(48 - 106*x + 21*x^2 + 78*x^3 - 47*x^4 + 3*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Aug 30 2018

Example

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

Crossrefs

Cf. A224550.

Sequence in context: A062902 A260106 A260099 * A247720 A204647 A260980

Adjacent sequences: A224543 A224544 A224545 * A224547 A224548 A224549

Keyword

nonn

Author

R. H. Hardin, Apr 10 2013

Status

approved