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A250443 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column.

%I A250443 #8 Jul 23 2025 12:25:24
%S A250443 81,324,324,1296,2160,1296,3600,14400,14400,3600,10000,60000,160000,
%T A250443 60000,10000,22500,250000,1000000,1000000,250000,22500,50625,787500,
%U A250443 6250000,8750000,6250000,787500,50625,99225,2480625,27562500,76562500
%N A250443 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column.
%C A250443 Table starts
%C A250443 .....81......324.......1296.........3600.........10000...........22500
%C A250443 ....324.....2160......14400........60000........250000..........787500
%C A250443 ...1296....14400.....160000......1000000.......6250000........27562500
%C A250443 ...3600....60000....1000000......8750000......76562500.......450187500
%C A250443 ..10000...250000....6250000.....76562500.....937890625......7353062500
%C A250443 ..22500...787500...27562500....450187500....7353062500.....74118870000
%C A250443 ..50625..2480625..121550625...2647102500...57648010000....747118209600
%C A250443 ..99225..6482700..423536400..11859019200..332052537600...5379251109120
%C A250443 .194481.16941456.1475789056..53128406016.1912622616576..38730607985664
%C A250443 .345744.38723328.4337012736.195165573120.8782450790400.217365657062400
%H A250443 R. H. Hardin, <a href="/A250443/b250443.txt">Table of n, a(n) for n = 1..262</a>
%F A250443 Empirical for column k, apparently a recurrence of order 8*k+8, and a polynomial of degree 4*k+4 plus a quasipolynomial of degree 4*k+2 with period 2:
%F A250443 k=1: [linear recurrence of order 16; also a polynomial of degree 8 plus a quasipolynomial of degree 6 with period 2]
%F A250443 k=2: [order 24; also a polynomial of degree 12 plus a quasipolynomial of degree 10 with period 2]
%F A250443 k=3: [order 32; also a polynomial of degree 16 plus a quasipolynomial of degree 14 with period 2]
%F A250443 k=4: [order 40; also a polynomial of degree 20 plus a quasipolynomial of degree 18 with period 2]
%F A250443 k=5: [order 48; also a polynomial of degree 24 plus a quasipolynomial of degree 22 with period 2]
%F A250443 k=6: [order 56; also a polynomial of degree 28 plus a quasipolynomial of degree 26 with period 2]
%F A250443 k=7: [order 64; also a polynomial of degree 32 plus a quasipolynomial of degree 30 with period 2]
%e A250443 Some solutions for n=3 k=4
%e A250443 ..0..0..0..0..0....0..0..0..2..0....0..0..0..2..0....0..0..0..0..0
%e A250443 ..0..0..1..0..2....0..0..1..1..1....0..0..0..0..0....0..2..2..2..2
%e A250443 ..0..2..0..2..2....0..2..0..2..1....0..1..0..2..1....1..0..2..1..2
%e A250443 ..2..1..2..2..2....0..0..2..2..2....0..0..1..2..2....0..2..2..2..2
%Y A250443 Column 1 is A250427
%K A250443 nonn,tabl
%O A250443 1,1
%A A250443 _R. H. Hardin_, Nov 22 2014