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

Author

R. H. Hardin, Dec 31 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A217873(n+1)

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