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

Author

R. H. Hardin Apr 10 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A204644

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