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T(n,k)=Number of length n+6 0..k arrays with no seven consecutive terms having six times any element equal to the sum of the remaining six
13

%I #6 Dec 12 2014 20:45:12

%S 126,1792,250,14336,4586,496,68712,51200,11874,984,249088,305908,

%T 183516,30876,1952,739284,1340288,1364252,658388,80354,3872,1898582,

%U 4669434,7224220,6089486,2362656,208876,7680,4361056,13824950,29549686,38980312

%N T(n,k)=Number of length n+6 0..k arrays with no seven consecutive terms having six times any element equal to the sum of the remaining six

%C Table starts

%C ...126....1792......14336.......68712.......249088.........739284

%C ...250....4586......51200......305908......1340288........4669434

%C ...496...11874.....183516.....1364252......7224220.......29549686

%C ...984...30876.....658388.....6089486.....38980312......187202568

%C ..1952...80354....2362656....27195324....210466508.....1186724138

%C ..3872..208876....8479940...121490228...1136802444.....7525617064

%C ..7680..541624...30441964...542821804...6141387290....47731565832

%C .15234.1400008..109315912..2425448642..33179587514...302750656716

%C .30218.3618986..392540302.10837998920.179264996934..1920348850344

%C .59940.9363890.1409749660.48432447004.968578232316.12181094726996

%H R. H. Hardin, <a href="/A249319/b249319.txt">Table of n, a(n) for n = 1..193</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4) +a(n-5) +a(n-6)

%F Empirical for row n:

%F n=1: [linear recurrence of order 19; also a polynomial of degree 7 plus a quasipolynomial of degree 0 with period 60]

%e Some solutions for n=3 k=4

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....0....1....1....1....0....0....1....1....0....1....1....1....1....0....0

%e ..3....2....3....2....1....3....2....0....0....1....2....2....3....0....3....0

%e ..2....3....0....0....2....2....3....3....3....0....4....2....3....2....3....0

%e ..1....2....2....2....1....2....2....4....1....3....3....3....2....4....4....2

%e ..3....1....0....3....1....3....3....2....3....4....2....1....1....2....4....4

%e ..2....4....2....4....4....1....0....3....4....2....0....0....0....4....4....2

%e ..0....0....3....4....0....1....3....4....4....1....4....0....1....2....2....4

%e ..0....0....3....0....1....1....2....2....0....1....2....0....3....3....2....0

%Y Column 1 is A249190

%Y Column 2 is A249191

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Oct 25 2014