A224548 Number of (n+1) X 7 0..1 matrices with each 2 X 2 subblock idempotent.

132, 218, 302, 448, 635, 916, 1323, 1941, 2887, 4363, 6688, 10383, 16288, 25764, 41012, 65594, 105273, 169374, 272985, 440519, 711477, 1149773, 1858822, 3005953, 4861910, 7864766, 12723338, 20584516, 33304007, 53884408, 87184023, 141063753

Offset

1,1

Comments

Column 6 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*(132 - 310*x + 90*x^2 + 198*x^3 - 129*x^4 + 10*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Aug 31 2018

Example

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

Crossrefs

Cf. A224550.

Sequence in context: A102474 A015235 A204649 * A253510 A253503 A195674

Adjacent sequences: A224545 A224546 A224547 * A224549 A224550 A224551

Keyword

nonn

Author

R. H. Hardin, Apr 10 2013

Status

approved