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A240756 Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of elements above it or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4. 1

%I

%S 5,6,12,16,16,35,35,36,65,83,102,172,191,230,381,458,576,905,1064,

%T 1362,2090,2514,3267,4869,5894,7740,11297,13853,18318,26249,32499,

%U 43165,60950,76216,101501,141589,178559,238124,328924,418014,557746,764306,977771

%N Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of elements above it or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

%H R. H. Hardin, <a href="/A240756/b240756.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-3) + a(n-5) - 2*a(n-8) - 4*a(n-9) - a(n-11) + 2*a(n-14) for n>17.

%F Empirical g.f.: x*(5 + 6*x + 12*x^2 + x^3 - 2*x^4 - 6*x^5 - 19*x^6 - 24*x^7 - 46*x^8 - 6*x^9 + 7*x^10 + 27*x^11 + 8*x^12 + 5*x^13 - 2*x^14 - x^15 - x^16) / ((1 + x)*(1 - x + x^2)*(1 - x^2 - x^3)*(1 - 2*x^3)*(1 + x^2 - x^3 + x^4 - x^5)). - _Colin Barker_, Oct 29 2018

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A240760.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2014

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Last modified January 17 20:06 EST 2022. Contains 350410 sequences. (Running on oeis4.)