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1/16 the number of (n+1) X 3 0..7 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.
2

%I #7 Oct 06 2015 22:07:24

%S 21,290,13169,550268,19849923,667017027,21320890377,659741463420,

%T 19939380387212,592112324464323,17343862233069362,502495529472928971,

%U 14428841233622907321,411240107421964502725,11647315145815312830954

%N 1/16 the number of (n+1) X 3 0..7 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

%C Column 2 of A183738.

%H R. H. Hardin, <a href="/A183731/b183731.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n)=59*a(n-1)-983*a(n-2)+1517*a(n-3)+56964*a(n-4)-301681*a(n-5)-391561*a(n-6)+6287597*a(n-7)-12340851*a(n-8)-17981853*a(n-9)+86923852*a(n-10)-42259832*a(n-11)-195169753*a(n-12)+251286677*a(n-13)+147371126*a(n-14)-407605405*a(n-15)+42991424*a(n-16)+309052737*a(n-17)-122546216*a(n-18)-125908592*a(n-19)+73571657*a(n-20)+29253790*a(n-21)-21987805*a(n-22)-3922294*a(n-23)+3666493*a(n-24)+284823*a(n-25)-339999*a(n-26)-7395*a(n-27)+16089*a(n-28)-300*a(n-29)-300*a(n-30)+16*a(n-31).

%e Some solutions with the first block increasing clockwise for 3 X 3:

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

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

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

%e ...

%e ...R..L.......R..R.......R..L.......R..L.......R..L.......R..R.......R..L...

%e ...R..L.......L..L.......R..L.......R..L.......R..L.......L..L.......R..L...

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 06 2011