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A229392 T(n,k)=Number of nXk 0..3 arrays of the sum of the corresponding element, the element to the east and the element to the south in a larger (n+1)X(k+1) 0..1 array.

%I A229392 #6 Jul 23 2025 05:42:59
%S A229392 4,14,14,48,128,48,164,1064,1064,164,560,8592,19124,8592,560,1912,
%T A229392 68672,319340,319340,68672,1912,6528,546752,5212236,10624396,5212236,
%U A229392 546752,6528,22288,4346752,84210828,345788172,345788172,84210828,4346752,22288
%N A229392 T(n,k)=Number of nXk 0..3 arrays of the sum of the corresponding element, the element to the east and the element to the south in a larger (n+1)X(k+1) 0..1 array.
%C A229392 Table starts
%C A229392 .....4........14...........48.............164................560
%C A229392 ....14.......128.........1064............8592..............68672
%C A229392 ....48......1064........19124..........319340............5212236
%C A229392 ...164......8592.......319340........10624396..........345788172
%C A229392 ...560.....68672......5212236.......345788172........22494002188
%C A229392 ..1912....546752.....84210828.....11156280332......1451228983308
%C A229392 ..6528...4346752...1353901580....358453456908.....93250181644300
%C A229392 .22288..34537984..21715025932..11493734735884...5979900142878732
%C A229392 .76096.274370048.347864379404.368171037655052.383094040360124428
%H A229392 R. H. Hardin, <a href="/A229392/b229392.txt">Table of n, a(n) for n = 1..287</a>
%F A229392 Empirical for column k:
%F A229392 k=1: a(n) = 4*a(n-1) -2*a(n-2)
%F A229392 k=2: a(n) = 12*a(n-1) -36*a(n-2) +32*a(n-3) -16*a(n-4)
%F A229392 k=3: a(n) = 25*a(n-1) -152*a(n-2) +144*a(n-3) -368*a(n-4) +1888*a(n-5) -1536*a(n-6) for n>9
%F A229392 k=4: a(n) = 49*a(n-1) -560*a(n-2) +544*a(n-3) -1568*a(n-4) +17920*a(n-5) -16384*a(n-6) for n>9
%F A229392 k=5: a(n) = 101*a(n-1) -2532*a(n-2) +10624*a(n-3) -8192*a(n-4) for n>7
%F A229392 k=6: a(n) = 193*a(n-1) -8384*a(n-2) +8320*a(n-3) -24704*a(n-4) +1073152*a(n-5) -1048576*a(n-6) for n>9
%F A229392 k=7: a(n) = 385*a(n-1) -33152*a(n-2) +33024*a(n-3) -98560*a(n-4) +8486912*a(n-5) -8388608*a(n-6) for n>9
%F A229392 k=8: a(n) = 777*a(n-1) -137992*a(n-2) +1185792*a(n-3) -1048576*a(n-4) for n>7
%F A229392 k=9: a(n) = 1537*a(n-1) -525824*a(n-2) +525312*a(n-3) -1573888*a(n-4) +538443776*a(n-5) -536870912*a(n-6) for n>9
%F A229392 k=10: a(n) = 3073*a(n-1) -2100224*a(n-2) +2099200*a(n-3) -6293504*a(n-4) +4301258752*a(n-5) -4294967296*a(n-6) for n>9
%F A229392 k=11: a(n) = 6161*a(n-1) -8493072*a(n-2) +142704640*a(n-3) -134217728*a(n-4) for n>7
%e A229392 Some solutions for n=3 k=4
%e A229392 ..1..1..0..1....1..1..1..3....0..1..1..2....0..1..2..3....0..0..2..1
%e A229392 ..0..0..1..0....3..2..1..2....2..1..0..0....2..2..2..2....0..1..2..1
%e A229392 ..1..2..2..1....3..1..2..3....2..1..0..1....2..0..2..3....0..1..2..3
%Y A229392 Column 1 is A007070
%K A229392 nonn,tabl
%O A229392 1,1
%A A229392 _R. H. Hardin_ Sep 21 2013