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A250437 Number of (n+1)X(2+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column.

%I A250437 #6 Jul 23 2025 12:24:41
%S A250437 324,2160,14400,60000,250000,787500,2480625,6482700,16941456,38723328,
%T A250437 88510464,182891520,377913600,721710000,1378265625,2470668750,
%U A250437 4428902500,7537186800,12826921536,20901168288,34057964304,53488469580,84004327225
%N A250437 Number of (n+1)X(2+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column.
%C A250437 Column 2 of A250443
%H A250437 R. H. Hardin, <a href="/A250437/b250437.txt">Table of n, a(n) for n = 1..210</a>
%F A250437 Empirical: a(n) = 2*a(n-1) +10*a(n-2) -22*a(n-3) -44*a(n-4) +110*a(n-5) +110*a(n-6) -330*a(n-7) -165*a(n-8) +660*a(n-9) +132*a(n-10) -924*a(n-11) +924*a(n-13) -132*a(n-14) -660*a(n-15) +165*a(n-16) +330*a(n-17) -110*a(n-18) -110*a(n-19) +44*a(n-20) +22*a(n-21) -10*a(n-22) -2*a(n-23) +a(n-24)
%F A250437 Empirical for n mod 2 = 0: a(n) = (1/2359296)*n^12 + (7/294912)*n^11 + (355/589824)*n^10 + (449/49152)*n^9 + (4541/49152)*n^8 + (1007/1536)*n^7 + (123317/36864)*n^6 + (113887/9216)*n^5 + (9439/288)*n^4 + (5837/96)*n^3 + (1197/16)*n^2 + (219/4)*n + 18
%F A250437 Empirical for n mod 2 = 1: a(n) = (1/2359296)*n^12 + (7/294912)*n^11 + (713/1179648)*n^10 + (2729/294912)*n^9 + (223799/2359296)*n^8 + (101131/147456)*n^7 + (2115031/589824)*n^6 + (2014145/147456)*n^5 + (88753375/2359296)*n^4 + (7180625/98304)*n^3 + (12440625/131072)*n^2 + (2428125/32768)*n + (6890625/262144)
%e A250437 Some solutions for n=4
%e A250437 ..0..2..0....0..0..1....0..0..0....0..1..0....0..1..0....1..0..2....0..1..0
%e A250437 ..0..1..2....0..1..0....1..0..2....0..1..1....0..2..0....0..1..1....0..0..2
%e A250437 ..0..2..2....1..2..1....0..1..1....1..1..2....0..1..1....1..1..2....0..1..1
%e A250437 ..2..2..2....2..1..2....1..1..2....2..2..2....1..2..2....0..2..2....1..0..2
%e A250437 ..0..2..2....1..2..2....1..2..1....1..1..2....1..1..1....2..1..2....1..1..2
%K A250437 nonn
%O A250437 1,1
%A A250437 _R. H. Hardin_, Nov 22 2014