A253397 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically

16, 44, 44, 96, 102, 96, 180, 143, 143, 180, 304, 197, 174, 197, 304, 476, 250, 246, 246, 250, 476, 704, 320, 316, 346, 316, 320, 704, 996, 391, 419, 465, 465, 419, 391, 996, 1360, 477, 520, 632, 666, 632, 520, 477, 1360, 1804, 564, 651, 823, 932, 932, 823, 651

Offset

1,1

Comments

Table starts

...16..44..96..180..304..476..704...996..1360..1804..2336..2964..3696..4540

...44.102.143..197..250..320..391...477...564...666...769...887..1006..1140

...96.143.174..246..316..419..520...651...780...939..1096..1283..1468..1683

..180.197.246..346..465..632..823..1071..1351..1695..2079..2535..3039..3623

..304.250.316..465..666..932.1269..1693..2201..2814..3527..4360..5309..6394

..476.320.419..632..932.1318.1855..2528..3408..4498..5864..7521..9542.11949

..704.391.520..823.1269.1855.2726..3810..5311..7163..9569.12493.16140.20493

..996.477.651.1071.1693.2528.3810..5396..7717.10593.14543.19463.25921.33918

.1360.564.780.1351.2201.3408.5311..7717.11392.15966.22500.30675.41701.55452

.1804.666.939.1695.2814.4498.7163.10593.15966.22634.32533.44959.62402.84560

Links

R. H. Hardin, Table of n, a(n) for n = 1..9654

Formula

Empirical for column k:

k=1: a(n) = (4/3)*n^3 + 4*n^2 + (20/3)*n + 4

k=2: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>8

k=3: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>8

k=4: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5) for n>11

k=5: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5) for n>13

k=6: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6) for n>16

k=7: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6) for n>18

Empirical quasipolynomials for column k:

k=2: polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2 for n>4

k=3: polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2 for n>4

k=4: polynomial of degree 3 plus a quasipolynomial of degree 0 with period 2 for n>6

k=5: polynomial of degree 3 plus a quasipolynomial of degree 0 with period 2 for n>8

k=6: polynomial of degree 4 plus a quasipolynomial of degree 0 with period 2 for n>10

k=7: polynomial of degree 4 plus a quasipolynomial of degree 0 with period 2 for n>12

Example

Some solutions for n=4 k=4
..1..1..1..1..1....0..0..0..0..0....0..0..0..1..1....0..1..0..1..1
..1..1..1..1..1....0..0..0..0..1....0..0..0..0..0....1..1..0..0..0
..1..1..1..1..1....0..0..0..0..1....0..0..0..0..1....1..1..1..1..1
..1..1..1..1..0....0..0..0..0..1....0..0..1..0..1....1..0..0..0..0
..0..1..1..1..1....0..0..0..0..1....1..0..1..0..1....1..1..1..1..1

Crossrefs

Column 1 is A217873(n+1)

Sequence in context: A088800 A316636 A187721 * A258554 A253326 A204039

Adjacent sequences: A253394 A253395 A253396 * A253398 A253399 A253400

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 31 2014

Status

approved