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A252271 Number of (n+2) X (1+2) 0..3 arrays with every 3 X 3 subblock row and column sum not equal to 2 3 4 6 or 7 and every 3 X 3 diagonal and antidiagonal sum equal to 2 3 4 6 or 7. 1

%I #8 Dec 03 2018 06:28:42

%S 206,185,232,322,535,852,1260,2221,3676,5538,9911,16558,25052,44989,

%T 75320,114066,204999,343366,520108,934893,1566072,2372290,4264343,

%U 7143510,10821116,19451805,32585288,49360882,88730215,148639302

%N Number of (n+2) X (1+2) 0..3 arrays with every 3 X 3 subblock row and column sum not equal to 2 3 4 6 or 7 and every 3 X 3 diagonal and antidiagonal sum equal to 2 3 4 6 or 7.

%H R. H. Hardin, <a href="/A252271/b252271.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-3) - 7*a(n-6) + 2*a(n-9) for n>12.

%F Empirical g.f.: x*(206 + 185*x + 232*x^2 - 914*x^3 - 575*x^4 - 540*x^5 + 770*x^6 + 306*x^7 + 188*x^8 - 180*x^9 - 40*x^10 + 2*x^11) / ((1 - x)*(1 + x + x^2)*(1 - 5*x^3 + 2*x^6)). - _Colin Barker_, Dec 03 2018

%e Some solutions for n=4:

%e ..2..3..0....0..3..2....3..2..3....2..3..0....3..0..2....3..2..0....2..1..2

%e ..1..2..2....3..3..2....2..1..2....2..3..3....2..2..1....0..0..1....3..2..3

%e ..2..3..3....2..2..1....3..2..0....1..2..2....3..3..2....2..3..0....0..2..3

%e ..2..3..3....3..3..2....3..2..3....2..3..3....3..0..2....3..2..0....2..1..2

%e ..1..2..2....0..3..2....2..1..2....2..0..3....2..2..1....0..0..0....3..2..3

%e ..2..0..3....2..2..1....0..2..3....1..2..2....0..3..2....2..3..0....3..2..0

%Y Column 1 of A252278.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 16 2014

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)