A234706 - OEIS

A234706

Number of (n+1) X (2+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 6 (constant-stress 1 X 1 tilings).

%I #6 Jun 20 2022 19:25:40

%S 1730,7154,28170,127586,546362,2630882,11903466,59901074,281693210,

%T 1465393634,7088270730,37835231666,186909507002,1018178950082,

%U 5110859386026,28298492397074,143792918144090,806722604366114

%N Number of (n+1) X (2+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 6 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234706/b234706.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) +159*a(n-2) -2412*a(n-3) -9452*a(n-4) +217248*a(n-5) +161262*a(n-6) -11578680*a(n-7) +10718427*a(n-8) +405901116*a(n-9) -824307633*a(n-10) -9828766476*a(n-11) +28650887914*a(n-12) +167599827384*a(n-13) -632763934044*a(n-14) -2003077953360*a(n-15) +9664372451624*a(n-16) +16138030431072*a(n-17) -105143721192576*a(n-18) -76625123046912*a(n-19) +819575849887488*a(n-20) +75093856109568*a(n-21) -4528143100320768*a(n-22) +1633754973450240*a(n-23) +17236678723430400*a(n-24) -11938042414080000*a(n-25) -42782336704512000*a(n-26) +40275310510080000*a(n-27) +62010467205120000*a(n-28) -70124998164480000*a(n-29) -39609913835520000*a(n-30) +50565847449600000*a(n-31).

%e Some solutions for n=4:

%e 5 0 6 0 0 1 6 2 7 1 6 1 4 7 3 2 6 2 6 2 5

%e 1 2 2 0 6 1 2 4 3 7 6 7 3 0 2 7 5 7 3 5 2

%e 5 0 6 6 6 7 5 1 6 1 6 1 2 5 1 2 6 2 5 1 4

%e 1 2 2 6 0 7 5 7 6 5 4 5 7 4 6 5 3 5 1 3 0

%e 6 1 7 4 4 5 5 1 6 1 6 1 1 4 0 2 6 2 5 1 4

%Y Column 2 of A234712.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 29 2013