A250646 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.

1, 1, 6, 1, 17, 6, 1, 36, 23, 20, 1, 65, 44, 125, 28, 1, 106, 89, 476, 280, 72, 1, 161, 134, 1293, 1424, 1061, 120, 1, 232, 219, 2954, 4853, 7696, 2870, 272, 1, 321, 296, 5901, 12473, 34441, 28238, 9495, 496, 1, 430, 433, 10766, 28379, 120114, 163043, 126482

Offset: 1

Author

R. H. Hardin, Nov 26 2014

Keywords

• nonn
• tabl

Comments

Table starts

......1.........1............1.............1...............1...............1

......6........17...........36............65.............106.............161

......6........23...........44............89.............134.............219

.....20.......125..........476..........1293............2954............5901

.....28.......280.........1424..........4853...........12473...........28379

.....72......1061.........7696.........34441..........120114..........332827

....120......2870........28238........163043..........677505.........2225195

....272......9495.......126482........915663.........4749950........18399217

....496.....27507.......491943.......4537317........28200435.......129137886

...1056.....86149......2059700......23671551.......177863786.......953809557

...2016....255704......8161068.....118358549......1063874048......6704767056

...4160....782393.....33268124.....601565301......6491819162.....47777146765

...8128...2341381....132637221....3011330309.....38892883673....335147823244

..16512...7090347....534771362...15155615651....234724691398...2360792885729

..32640..21271463...2136620867...75845220727...1407192408230..16540740396740

..65792..64109181...8574987528..380253505733...8460554956974.116054610957529

.130816.192439733..34285733053.1902264449049..50741165814612.812699929957712

.262656.578665211.137334914170.9522274036139.304671802762820

Examples

			Some solutions for n=5 k=4
..4....2....1....4....0....1....1....2....0....2....1....2....2....4....4....3
..1....1....1....1....2....2....0....2....0....1....0....1....2....0....1....3
..1....0....1....1....2....0....0....1....1....0....2....0....2....2....0....1
..0....1....0....0....0....0....1....1....2....4....3....4....1....3....2....2
..1....1....1....3....1....4....3....0....1....3....3....3....1....0....1....4
..3....0....4....3....3....3....3....0....0....2....0....3....3....2....0....4
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..267

Crossrefs

Column 1 is A113979(n+2)

Row 2 is A084990(n+1)

Formula

Empirical for column k:

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

k=2: [order 10]

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

Empirical for row n:

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

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

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

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

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