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A253455 Number of (n+1) X (7+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically. 1

%I #7 Dec 13 2018 09:15:36

%S 48293,74324,89556,114717,170184,285681,526430,1036512,2142374,

%T 4611192,10320110,24051792,58456694,148091112,389833790,1060740672,

%U 2964819014,8459769432,24510051470,71791759152,211898605334,628742590152

%N Number of (n+1) X (7+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.

%H R. H. Hardin, <a href="/A253455/b253455.txt">Table of n, a(n) for n = 1..147</a>

%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>9.

%F Empirical: a(n) = 529*3^(n-3) + 6631*2^(n-1) + 59197 for n>6.

%F Empirical g.f.: x*(48293 - 215434*x + 174835*x^2 + 105187*x^3 + 21054*x^4 - 10872*x^5 - 3934*x^6 - 681*x^7 - 54*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Dec 13 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 7 of A253456.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 01 2015

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Last modified March 4 11:14 EST 2024. Contains 370528 sequences. (Running on oeis4.)