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

1,3

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A113979(n+2)

Row 2 is A084990(n+1)

Sequence in context: A278863 A281413 A049325 * A277068 A369904 A373573

Adjacent sequences: A250643 A250644 A250645 * A250647 A250648 A250649

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 26 2014

Status

approved