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A251048 Number of (n+1) X (1+1) 0..3 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the absolute difference of its antidiagonal elements. 1

%I #8 Nov 24 2018 08:12:59

%S 66,290,854,2243,5449,12858,29759,68506,157205,360885,828728,1904810,

%T 4380530,10079260,23198280,53404661,122956951,283114508,651911889,

%U 1501161236,3456777827,7960112783,18330262426,42210375756,97200890000

%N Number of (n+1) X (1+1) 0..3 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

%H R. H. Hardin, <a href="/A251048/b251048.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 18*a(n-2) + 17*a(n-3) + 10*a(n-4) - 39*a(n-5) + 38*a(n-6) - 17*a(n-7) + 3*a(n-8) for n>9.

%F Empirical g.f.: x*(66 - 172*x + 12*x^2 + 363*x^3 - 470*x^4 + 245*x^5 - 34*x^6 - 18*x^7 + 6*x^8) / ((1 - x)^6*(1 - x - 3*x^2)). - _Colin Barker_, Nov 24 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A251055.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 29 2014

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Last modified February 22 15:38 EST 2024. Contains 370256 sequences. (Running on oeis4.)