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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 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 22 10:56 EDT 2022. Contains 353949 sequences. (Running on oeis4.)