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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.)