A250646 - OEIS

%I #6 Dec 12 2014 20:49:57

%S 1,1,6,1,17,6,1,36,23,20,1,65,44,125,28,1,106,89,476,280,72,1,161,134,

%T 1293,1424,1061,120,1,232,219,2954,4853,7696,2870,272,1,321,296,5901,

%U 12473,34441,28238,9495,496,1,430,433,10766,28379,120114,163043,126482

%N T(n,k)=Number of length n+1 0..k arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero

%C Table starts

%C ......1.........1............1.............1...............1...............1

%C ......6........17...........36............65.............106.............161

%C ......6........23...........44............89.............134.............219

%C .....20.......125..........476..........1293............2954............5901

%C .....28.......280.........1424..........4853...........12473...........28379

%C .....72......1061.........7696.........34441..........120114..........332827

%C ....120......2870........28238........163043..........677505.........2225195

%C ....272......9495.......126482........915663.........4749950........18399217

%C ....496.....27507.......491943.......4537317........28200435.......129137886

%C ...1056.....86149......2059700......23671551.......177863786.......953809557

%C ...2016....255704......8161068.....118358549......1063874048......6704767056

%C ...4160....782393.....33268124.....601565301......6491819162.....47777146765

%C ...8128...2341381....132637221....3011330309.....38892883673....335147823244

%C ..16512...7090347....534771362...15155615651....234724691398...2360792885729

%C ..32640..21271463...2136620867...75845220727...1407192408230..16540740396740

%C ..65792..64109181...8574987528..380253505733...8460554956974.116054610957529

%C .130816.192439733..34285733053.1902264449049..50741165814612.812699929957712

%C .262656.578665211.137334914170.9522274036139.304671802762820

%H R. H. Hardin, <a href="/A250646/b250646.txt">Table of n, a(n) for n = 1..267</a>

%F Empirical for column k:

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

%F k=2: [order 10]

%F k=3: [order 24] for n>25

%F Empirical for row n:

%F n=1: a(n) = a(n-1)

%F n=2: a(n) = (1/3)*n^3 + 2*n^2 + (8/3)*n + 1

%F n=3: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7); also a polynomial of degree 3 plus a quasipolynomial of degree 2 with period 2

%F n=4: [order 14; also a polynomial of degree 5 plus a quasipolynomial of degree 2 with period 6]

%F n=5: [order 25; also a polynomial of degree 5 plus a quasipolynomial of degree 4 with period 12]

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 1 is A113979(n+2)

%Y Row 2 is A084990(n+1)

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Nov 26 2014