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Number of (n+1)X(1+1) 0..2 arrays with the maximum plus the minimum minus the lower median of every 2X2 subblock equal
+10
1
81, 327, 1386, 6093, 27079, 121590, 549173, 2495215, 11389842, 52223381, 240352711, 1110041358, 5141952693, 23882414527, 111181569882, 518644232789, 2423637273943, 11342969544566, 53156257829813, 249385929539023
FORMULA
Empirical: a(n) = 9*a(n-1) -2*a(n-2) -167*a(n-3) +265*a(n-4) +1110*a(n-5) -2280*a(n-6) -3350*a(n-7) +7924*a(n-8) +4700*a(n-9) -13072*a(n-10) -2560*a(n-11) +9856*a(n-12) +128*a(n-13) -2560*a(n-14)
EXAMPLE
Some solutions for n=5
..1..2....2..1....1..1....2..2....2..1....0..2....1..0....0..1....0..2....1..1
..0..2....2..2....0..0....2..2....2..1....1..1....2..2....2..2....1..1....2..1
..1..1....1..0....1..0....2..2....2..1....1..1....2..1....0..1....2..0....1..2
..2..0....0..1....2..1....0..0....1..2....1..1....0..1....0..1....2..1....1..2
..1..1....2..2....2..2....2..1....2..1....2..0....1..2....1..2....0..1....2..1
..1..1....1..0....1..0....0..0....1..1....2..1....0..1....2..0....2..1....0..0
Number of (n+1)X(2+1) 0..2 arrays with the maximum plus the minimum minus the lower median of every 2X2 subblock equal
+10
1
327, 2211, 15254, 109205, 786609, 5747502, 42215123, 312592339, 2324534826, 17376767995, 130331607713, 981030661960, 7403192678283, 56006537652545, 424502700379214, 3223178794593881, 24506960972636245, 186565676015487922
FORMULA
Empirical: a(n) = 20*a(n-1) -74*a(n-2) -950*a(n-3) +7675*a(n-4) +5902*a(n-5) -208583*a(n-6) +358712*a(n-7) +2437168*a(n-8) -8245218*a(n-9) -11507689*a(n-10) +77981588*a(n-11) -13353740*a(n-12) -390127858*a(n-13) +398463912*a(n-14) +1060576100*a(n-15) -1911844548*a(n-16) -1338399672*a(n-17) +4592202520*a(n-18) -205399632*a(n-19) -6115028512*a(n-20) +2874814400*a(n-21) +4321062784*a(n-22) -3582260416*a(n-23) -1253904064*a(n-24) +1886965760*a(n-25) -92450688*a(n-26) -394737408*a(n-27) +90316800*a(n-28) +17190912*a(n-29) -4915200*a(n-30)
EXAMPLE
Some solutions for n=4
..0..1..2....1..2..0....2..0..0....2..1..0....2..1..0....2..1..0....2..0..1
..1..0..1....1..2..0....2..1..1....0..2..2....2..2..1....1..0..1....2..1..2
..1..0..1....0..0..0....2..2..0....1..2..1....0..1..0....1..2..2....0..2..0
..0..0..0....1..2..1....0..1..2....0..1..0....1..0..1....2..0..1....1..2..1
..0..1..1....2..1..2....0..0..2....2..2..2....2..2..1....1..2..2....2..0..1
Number of (n+1)X(3+1) 0..2 arrays with the maximum plus the minimum minus the lower median of every 2X2 subblock equal
+10
1
1386, 15254, 168564, 1949236, 22695802, 269108894, 3207539588, 38599508572, 466275664500, 5664487537556, 69007333422447, 843652458439362, 10335176759901673, 126898784204316940, 1560376523474291714
FORMULA
Empirical recurrence of order 84 (see link above)
EXAMPLE
Some solutions for n=3
..0..2..2..0....0..1..0..1....0..2..0..2....1..1..0..0....1..0..2..2
..0..0..0..1....2..2..2..1....0..0..0..0....0..0..1..0....2..0..0..0
..2..2..0..2....2..1..0..1....0..2..0..2....0..1..0..1....0..1..2..1
..1..1..0..2....0..2..2..1....0..0..0..0....0..0..0..0....0..2..1..2
Number of (n+1)X(4+1) 0..2 arrays with the maximum plus the minimum minus the lower median of every 2X2 subblock equal
+10
1
6093, 109205, 1949236, 36874967, 701424751, 13643698414, 266389315989, 5258599354623, 104078580277828, 2072356525693189, 41343357985843129, 827681012692523870, 16593350093477339371, 333360416125702959021
EXAMPLE
Some solutions for n=2
..0..0..2..1..0....2..1..2..2..2....1..0..2..0..1....2..1..0..2..2
..1..1..1..0..0....0..1..0..1..2....2..0..0..2..0....0..1..2..1..0
..1..1..1..0..1....0..1..0..0..2....0..0..2..0..0....2..1..0..2..1
Number of (n+1)X(5+1) 0..2 arrays with the maximum plus the minimum minus the lower median of every 2X2 subblock equal
+10
1
27079, 786609, 22695802, 701424751, 21755065689, 692297987804, 22074170878628, 712496076337427, 23029391418201045, 749146158534878661, 24396571520181638506, 797305500866630422916, 26078978852511028113590
EXAMPLE
Some solutions for n=1
..1..1..1..0..1..2....1..2..0..2..2..2....2..0..1..2..1..0....0..1..1..1..1..2
..2..0..0..0..0..1....0..2..1..2..1..2....1..1..0..1..0..0....1..2..0..2..0..1
Number of (n+1) X (6+1) 0..2 arrays with the maximum plus the minimum minus the lower median of every 2 X 2 subblock equal.
+10
1
121590, 5747502, 269108894, 13643698414, 692297987804, 36178398554012, 1890491225892878, 100148557160615280, 5305466920253259264, 283011393021083999606, 15099947793285680101269, 808583766977800373774476
EXAMPLE
Some solutions for n=1
..0..0..2..2..2..0..1....1..0..1..0..1..1..0....0..2..0..2..2..0..2
..0..1..1..0..1..1..0....0..1..0..1..0..2..1....1..0..0..1..1..0..2
Number of (n+1)X(7+1) 0..2 arrays with the maximum plus the minimum minus the lower median of every 2X2 subblock equal
+10
1
549173, 42215123, 3207539588, 266389315989, 22074170878628, 1890491225892878, 161548363232714369, 14015229199452065845, 1214266240157296815136, 105989693767809487599852, 9245561984165022603050940
EXAMPLE
Some solutions for n=1
..0..1..2..1..2..0..0..1....0..0..1..1..2..0..0..1....0..1..2..1..1..1..0..1
..0..0..1..0..1..1..0..0....1..0..0..0..1..1..0..1....1..0..1..0..2..0..1..2
Number of (n+1)X(n+1) 0..2 arrays with the maximum plus the minimum minus the lower median of every 2X2 subblock equal
+10
0
81, 2211, 168564, 36874967, 21755065689, 36178398554012, 161548363232714369, 1994329748960606374641
EXAMPLE
Some solutions for n=3
..1..0..0..0....1..0..1..0....1..0..1..0....1..1..0..2....0..0..2..2
..1..0..1..1....2..1..2..2....1..2..2..2....2..0..1..2....1..1..1..2
..2..2..1..1....0..1..0..1....1..0..1..0....2..1..2..0....0..2..0..2
..1..0..2..0....1..2..2..1....1..2..2..1....2..0..2..1....1..2..1..1
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