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A250671 Number of (n+1)X(3+1) 0..3 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

%I A250671 #6 Jul 23 2025 12:40:02
%S A250671 3927,42422,388916,3107446,22408818,148821788,923242475,5408914174,
%T A250671 30183160828,161540947652,833948226614,4172559026594,20315088999198,
%U A250671 96576921782616,449613162886204,2055003400985552,9241542539124820
%N A250671 Number of (n+1)X(3+1) 0..3 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
%C A250671 Column 3 of A250676
%H A250671 R. H. Hardin, <a href="/A250671/b250671.txt">Table of n, a(n) for n = 1..210</a>
%F A250671 Empirical: a(n) = 65*a(n-1) -2040*a(n-2) +41182*a(n-3) -601025*a(n-4) +6757461*a(n-5) -60904682*a(n-6) +452104888*a(n-7) -2818259682*a(n-8) +14967704738*a(n-9) -68478620392*a(n-10) +272205579828*a(n-11) -946422923082*a(n-12) +2893259719938*a(n-13) -7808288819292*a(n-14) +18659986712520*a(n-15) -39573170147037*a(n-16) +74582440486893*a(n-17) -125002834972016*a(n-18) +186317017612318*a(n-19) -246795421123605*a(n-20) +290111846304617*a(n-21) -301991734906378*a(n-22) +277530162730704*a(n-23) -224266440175648*a(n-24) +158524442376560*a(n-25) -97366518380640*a(n-26) +51522457118080*a(n-27) -23231309452544*a(n-28) +8797779121920*a(n-29) -2744576054784*a(n-30) +686513332224*a(n-31) -132324212736*a(n-32) +18444423168*a(n-33) -1654235136*a(n-34) +71663616*a(n-35) for n>47
%e A250671 Some solutions for n=2
%e A250671 ..2..1..0..2....0..0..1..1....2..1..0..0....1..2..0..2....1..1..0..3
%e A250671 ..2..1..1..1....0..0..1..2....2..1..2..3....0..3..2..0....1..1..0..3
%e A250671 ..2..2..2..2....1..2..3..0....3..0..3..2....1..2..3..1....2..0..1..2
%K A250671 nonn
%O A250671 1,1
%A A250671 _R. H. Hardin_, Nov 26 2014