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A224550 T(n,k)=Number of (n+1)X(k+1) 0..1 matrices with each 2X2 subblock idempotent 8
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 (list; table; graph; refs; listen; history; text; internal format)
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 A319317

Adjacent sequences:  A224547 A224548 A224549 * A224551 A224552 A224553

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Apr 10 2013

STATUS

approved

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Last modified December 4 19:40 EST 2021. Contains 349526 sequences. (Running on oeis4.)