A224550 T(n,k)=Number of (n+1)X(k+1) 0..1 matrices with each 2X2 subblock idempotent

8, 16, 16, 28, 32, 28, 48, 52, 52, 48, 80, 86, 78, 86, 80, 132, 137, 125, 125, 137, 132, 216, 218, 193, 196, 193, 218, 216, 352, 345, 302, 294, 294, 302, 345, 352, 572, 547, 472, 448, 428, 448, 472, 547, 572, 928, 869, 743, 682, 635, 635, 682, 743, 869, 928, 1504, 1385

Offset

1,1

Comments

Table starts

...8...16...28...48...80..132..216..352..572...928..1504..2436..3944..6384

..16...32...52...86..137..218..345..547..869..1385..2214..3549..5702..9178

..28...52...78..125..193..302..472..743.1175..1868..2982..4777..7673.12350

..48...86..125..196..294..448..682.1049.1626..2543..4007..6355.10131.16216

..80..137..193..294..428..635..943.1420.2162..3333..5193..8166.12936.20611

.132..218..302..448..635..916.1323.1941.2887..4363..6688.10383.16288.25764

.216..345..472..682..943.1323.1858.2652.3845..5681..8544.13062.20247.31739

.352..547..743.1049.1420.1941.2652.3678.5184..7460.10961.16432.25073.38829

.572..869.1175.1626.2162.2887.3845.5184.7096..9921.14191.20778.31086.47391

.928.1385.1868.2543.3333.4363.5681.7460.9921.13458.18686.26614.38866.58075

Acceptable 2X2 patterns

..1..0....1..1....0..0....0..0....1..0....1..0....0..1....0..0

..0..1....0..0....0..1....1..1....1..0....0..0....0..1....0..0

Forbidden 2X2 patterns

..1..1....0..1....1..0....0..1....1..1....0..0....1..1....0..1

..1..0....1..0....1..1....1..1....1..1....1..0....0..1....0..0

Links

R. H. Hardin, Table of n, a(n) for n = 1..1103

Formula

Empirical for diagonal:

a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9)

Empirical for column k:

k=1: a(n) = 2*a(n-1) -a(n-3)

k=2: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5)

k=3..12+: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5) for n>6

Example

Some solutions for n=3 k=4
..1..1..0..0..0....1..0..1..0..1....1..0..0..0..0....1..0..1..0..0
..0..0..0..0..0....1..0..1..0..1....1..0..0..0..0....1..0..1..0..0
..1..1..1..1..1....0..0..1..0..1....0..0..0..0..0....1..0..1..0..0
..0..0..0..0..0....0..0..1..0..1....0..0..0..1..1....0..0..1..0..1

Crossrefs

Column 1 is A204644

Sequence in context: A238835 A040056 A242890 * A204651 A203452 A363982

Adjacent sequences: A224547 A224548 A224549 * A224551 A224552 A224553

Keyword

nonn,tabl

Author

R. H. Hardin Apr 10 2013

Status

approved