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Number of (n+1)X(2+1) 0..2 arrays with every 2X2 subblock sum differing from its neighbors horizontally, vertically, diagonally and antidiagonally
1

%I #4 Dec 29 2014 19:14:45

%S 558,3600,23546,167832,1184928,8243488,57474376,402165016,2811886280,

%T 19648735840,137308874176,959744819720,6708131042848,46884212361800,

%U 327678437410752,2290232105294136,16007076725008072,111877100758327680

%N Number of (n+1)X(2+1) 0..2 arrays with every 2X2 subblock sum differing from its neighbors horizontally, vertically, diagonally and antidiagonally

%C Column 2 of A253294

%H R. H. Hardin, <a href="/A253290/b253290.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +22*a(n-2) -47*a(n-3) +847*a(n-4) -2548*a(n-5) -14241*a(n-6) +46156*a(n-7) -235684*a(n-8) +513456*a(n-9) +3142562*a(n-10) -12248092*a(n-11) +34872668*a(n-12) -44225096*a(n-13) -327631492*a(n-14) +1356943312*a(n-15) -3049192352*a(n-16) +2235968632*a(n-17) +17503809584*a(n-18) -67675653456*a(n-19) +140372058144*a(n-20) -119547407360*a(n-21) -386660564160*a(n-22) +1410208318912*a(n-23) -2855898321408*a(n-24) +4453728916224*a(n-25) -381216535552*a(n-26) -12897724549120*a(n-27) +35949674973184*a(n-28) -73144228077568*a(n-29) +67153529954304*a(n-30) +54469989974016*a(n-31) -290876893462528*a(n-32) +505744121200640*a(n-33) -360592985554944*a(n-34) -244530708480000*a(n-35) +1126160419258368*a(n-36) -1315197520183296*a(n-37) -66806203023360*a(n-38) +1063245997670400*a(n-39) -489223618560000*a(n-40)

%e Some solutions for n=4

%e ..0..1..1....0..0..1....1..0..0....0..0..1....1..0..0....1..2..0....1..2..1

%e ..0..0..2....0..0..2....1..0..0....1..2..2....0..1..0....2..2..1....0..2..2

%e ..0..0..1....1..0..0....1..1..0....1..2..2....1..1..2....0..0..0....0..0..2

%e ..0..2..1....0..2..2....0..2..2....0..1..0....1..2..1....0..1..1....0..1..0

%e ..0..1..2....0..0..2....2..2..1....0..1..1....0..0..1....2..0..2....2..1..0

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 29 2014