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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.

%I A253397 #9 Jul 23 2025 14:01:50
%S A253397 16,44,44,96,102,96,180,143,143,180,304,197,174,197,304,476,250,246,
%T A253397 246,250,476,704,320,316,346,316,320,704,996,391,419,465,465,419,391,
%U A253397 996,1360,477,520,632,666,632,520,477,1360,1804,564,651,823,932,932,823,651
%N 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.
%C A253397 Table starts
%C A253397 ...16..44..96..180..304..476..704...996..1360..1804..2336..2964..3696..4540
%C A253397 ...44.102.143..197..250..320..391...477...564...666...769...887..1006..1140
%C A253397 ...96.143.174..246..316..419..520...651...780...939..1096..1283..1468..1683
%C A253397 ..180.197.246..346..465..632..823..1071..1351..1695..2079..2535..3039..3623
%C A253397 ..304.250.316..465..666..932.1269..1693..2201..2814..3527..4360..5309..6394
%C A253397 ..476.320.419..632..932.1318.1855..2528..3408..4498..5864..7521..9542.11949
%C A253397 ..704.391.520..823.1269.1855.2726..3810..5311..7163..9569.12493.16140.20493
%C A253397 ..996.477.651.1071.1693.2528.3810..5396..7717.10593.14543.19463.25921.33918
%C A253397 .1360.564.780.1351.2201.3408.5311..7717.11392.15966.22500.30675.41701.55452
%C A253397 .1804.666.939.1695.2814.4498.7163.10593.15966.22634.32533.44959.62402.84560
%H A253397 R. H. Hardin, <a href="/A253397/b253397.txt">Table of n, a(n) for n = 1..9654</a>
%F A253397 Empirical for column k:
%F A253397 k=1: a(n) = (4/3)*n^3 + 4*n^2 + (20/3)*n + 4
%F A253397 k=2: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>8
%F A253397 k=3: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>8
%F A253397 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
%F A253397 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
%F A253397 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
%F A253397 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
%F A253397 Empirical quasipolynomials for column k:
%F A253397 k=2: polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2 for n>4
%F A253397 k=3: polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2 for n>4
%F A253397 k=4: polynomial of degree 3 plus a quasipolynomial of degree 0 with period 2 for n>6
%F A253397 k=5: polynomial of degree 3 plus a quasipolynomial of degree 0 with period 2 for n>8
%F A253397 k=6: polynomial of degree 4 plus a quasipolynomial of degree 0 with period 2 for n>10
%F A253397 k=7: polynomial of degree 4 plus a quasipolynomial of degree 0 with period 2 for n>12
%e A253397 Some solutions for n=4 k=4
%e A253397 ..1..1..1..1..1....0..0..0..0..0....0..0..0..1..1....0..1..0..1..1
%e A253397 ..1..1..1..1..1....0..0..0..0..1....0..0..0..0..0....1..1..0..0..0
%e A253397 ..1..1..1..1..1....0..0..0..0..1....0..0..0..0..1....1..1..1..1..1
%e A253397 ..1..1..1..1..0....0..0..0..0..1....0..0..1..0..1....1..0..0..0..0
%e A253397 ..0..1..1..1..1....0..0..0..0..1....1..0..1..0..1....1..1..1..1..1
%Y A253397 Column 1 is A217873(n+1)
%K A253397 nonn,tabl
%O A253397 1,1
%A A253397 _R. H. Hardin_, Dec 31 2014