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%I #6 Nov 25 2014 20:21:12
%S 19683,157464,1259712,10077696,46656000,216000000,1000000000,
%T 3375000000,11390625000,38443359375,105488578125,289460658375,
%U 794280046581,1882737888192,4462786105344,10578455953408,22483074023424
%N Number of (n+2)X(1+2) 0..2 arrays with nondecreasing sum of every three consecutive values in every row and column
%C Column 1 of A250601
%H R. H. Hardin, <a href="/A250594/b250594.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) -a(n-2) +17*a(n-3) -34*a(n-4) +17*a(n-5) -136*a(n-6) +272*a(n-7) -136*a(n-8) +680*a(n-9) -1360*a(n-10) +680*a(n-11) -2380*a(n-12) +4760*a(n-13) -2380*a(n-14) +6188*a(n-15) -12376*a(n-16) +6188*a(n-17) -12376*a(n-18) +24752*a(n-19) -12376*a(n-20) +19448*a(n-21) -38896*a(n-22) +19448*a(n-23) -24310*a(n-24) +48620*a(n-25) -24310*a(n-26) +24310*a(n-27) -48620*a(n-28) +24310*a(n-29) -19448*a(n-30) +38896*a(n-31) -19448*a(n-32) +12376*a(n-33) -24752*a(n-34) +12376*a(n-35) -6188*a(n-36) +12376*a(n-37) -6188*a(n-38) +2380*a(n-39) -4760*a(n-40) +2380*a(n-41) -680*a(n-42) +1360*a(n-43) -680*a(n-44) +136*a(n-45) -272*a(n-46) +136*a(n-47) -17*a(n-48) +34*a(n-49) -17*a(n-50) +a(n-51) -2*a(n-52) +a(n-53)
%F Empirical for n mod 3 = 0: a(n) = (1/198359290368)*n^18 + (13/22039921152)*n^17 + (119/3673320192)*n^16 + (1019/918330048)*n^15 + (3613/136048896)*n^14 + (21383/45349632)*n^13 + (16213/2519424)*n^12 + (43469/629856)*n^11 + (220013/373248)*n^10 + (40699235/10077696)*n^9 + (12452611/559872)*n^8 + (2290913/23328)*n^7 + (251452/729)*n^6 + (410549/432)*n^5 + (48193/24)*n^4 + (6277/2)*n^3 + (6831/2)*n^2 + (4617/2)*n + 729
%F Empirical for n mod 3 = 1: a(n) = (1/198359290368)*n^18 + (13/22039921152)*n^17 + (179/5509980288)*n^16 + (18499/16529940864)*n^15 + (297767/11019960576)*n^14 + (5350891/11019960576)*n^13 + (111248963/16529940864)*n^12 + (405352597/5509980288)*n^11 + (14169500801/22039921152)*n^10 + (897624081133/198359290368)*n^9 + (70847504005/2754990144)*n^8 + (10133814925/86093442)*n^7 + (55624481500/129140163)*n^6 + (53508910000/43046721)*n^5 + (119106800000/43046721)*n^4 + (591968000000/129140163)*n^3 + (229120000000/43046721)*n^2 + (166400000000/43046721)*n + (512000000000/387420489)
%F Empirical for n mod 3 = 2: a(n) = (1/198359290368)*n^18 + (13/22039921152)*n^17 + (119/3673320192)*n^16 + (2293/2066242608)*n^15 + (292783/11019960576)*n^14 + (192665/408146688)*n^13 + (53309863/8264970432)*n^12 + (381843511/5509980288)*n^11 + (4359976739/7346640384)*n^10 + (809482556189/198359290368)*n^9 + (248884779899/11019960576)*n^8 + (184314415957/1836660096)*n^7 + (2936802782977/8264970432)*n^6 + (170285851687/172186884)*n^5 + (40480785569/19131876)*n^4 + (433623389962/129140163)*n^3 + (160212055220/43046721)*n^2 + (36894726400/14348907)*n + (322828856000/387420489)
%e Some solutions for n=2
%e ..1..0..0....0..0..0....0..0..2....0..1..0....0..0..2....0..1..2....1..0..1
%e ..0..2..1....1..1..1....0..0..2....0..1..2....0..1..0....1..2..1....2..2..0
%e ..0..1..0....1..1..2....2..2..0....1..1..1....2..2..1....1..2..1....0..0..1
%e ..1..2..2....0..1..1....0..2..2....1..1..1....2..0..2....0..1..2....2..1..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 25 2014
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