A234733 - OEIS

A234733

Number of (n+1) X (3+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 8 (constant-stress 1 X 1 tilings).

%I #6 Jun 20 2022 18:53:59

%S 2184,6048,14760,45792,127032,423072,1283880,4481376,14469624,

%T 52195488,176064360,650582112,2265751992,8525288352,30415487400,

%U 116039804256,421792852344,1626492482208,5999520374760,23327294132832,87053575664952

%N Number of (n+1) X (3+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 8 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234733/b234733.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) +53*a(n-2) -564*a(n-3) -888*a(n-4) +17184*a(n-5) -2382*a(n-6) -296784*a(n-7) +308859*a(n-8) +3196608*a(n-9) -5284083*a(n-10) -22169196*a(n-11) +48357478*a(n-12) +97763896*a(n-13) -273091508*a(n-14) -253071696*a(n-15) +976703832*a(n-16) +271829664*a(n-17) -2148744960*a(n-18) +304750080*a(n-19) +2640988800*a(n-20) -1133222400*a(n-21) -1378944000*a(n-22) +870912000*a(n-23).

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 3 of A234738.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 30 2013