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A251888 Number of (n+2) X (2+2) 0..3 arrays with every 3 X 3 subblock row and column sum not 2 3 6 or 7 and every diagonal and antidiagonal sum 2 3 6 or 7. 1

%I #7 Nov 30 2018 10:05:21

%S 1664,1232,602,530,594,790,1182,1670,2474,3890,5642,8594,13922,20498,

%T 31778,52418,77858,121922,203138,303170,477314,799490,1196162,1888514,

%U 3171842,4751618,7512578,12635138,18940418,29967362,50436098,75629570

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

%H R. H. Hardin, <a href="/A251888/b251888.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 6*a(n-3) - 6*a(n-4) - 8*a(n-6) + 8*a(n-7) for n>14.

%F Empirical g.f.: 2*x*(832 - 216*x - 315*x^2 - 5028*x^3 + 1328*x^4 + 1988*x^5 + 7068*x^6 - 1676*x^7 - 2706*x^8 - 756*x^9 - 332*x^10 - 152*x^11 - 16*x^12 - 16*x^13) / ((1 - x)*(1 - 2*x^3)*(1 - 4*x^3)). - _Colin Barker_, Nov 30 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 2 of A251894.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 10 2014

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Last modified April 14 07:36 EDT 2024. Contains 371655 sequences. (Running on oeis4.)