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A251974 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column.

%I A251974 #8 Jul 23 2025 13:35:59
%S A251974 256,1600,1600,10000,20000,10000,40000,250000,250000,40000,160000,
%T A251974 1750000,6250000,1750000,160000,490000,12250000,76562500,76562500,
%U A251974 12250000,490000,1500625,60025000,937890625,1500625000,937890625
%N A251974 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column.
%C A251974 Table starts
%C A251974 .....256......1600.......10000.........40000..........160000............490000
%C A251974 ....1600.....20000......250000.......1750000........12250000..........60025000
%C A251974 ...10000....250000.....6250000......76562500.......937890625........7353062500
%C A251974 ...40000...1750000....76562500....1500625000.....29412250000......345888060000
%C A251974 ..160000..12250000...937890625...29412250000....922368160000....16270574342400
%C A251974 ..490000..60025000..7353062500..345888060000..16270574342400...410018473428480
%C A251974 .1500625.294122500.57648010000.4067643585600.287012931399936.10332465530397696
%H A251974 R. H. Hardin, <a href="/A251974/b251974.txt">Table of n, a(n) for n = 1..160</a>
%F A251974 Empirical for column k:
%F A251974 k=1: [linear recurrence of order 24; also a polynomial of degree 12 plus a quasipolynomial of degree 10 with period 2]
%F A251974 k=2: [order 36; also a polynomial of degree 18 plus a quasipolynomial of degree 16 with period 2]
%F A251974 k=3: [order 48; also a polynomial of degree 24 plus a quasipolynomial of degree 22 with period 2]
%F A251974 k=4: [polynomial of degree 30 plus a quasipolynomial of degree 28 with period 2]
%e A251974 Some solutions for n=2 k=4
%e A251974 ..0..0..0..1..0....1..1..1..1..2....1..0..1..1..1....0..0..0..0..0
%e A251974 ..1..0..1..0..3....1..0..2..0..2....0..0..0..0..2....0..0..0..0..0
%e A251974 ..2..1..2..1..2....2..2..2..2..3....1..3..2..3..2....2..1..2..2..3
%Y A251974 Column 1 is A250429
%Y A251974 Column 3 is A250440
%K A251974 nonn,tabl
%O A251974 1,1
%A A251974 _R. H. Hardin_, Dec 12 2014