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A251230 Number of (n+1) X (2+1) 0..3 arrays with every 2 X 2 subblock summing to 6 and no 2 X 2 subblock having exactly two nonzero entries. 1

%I #14 Nov 27 2018 09:01:00

%S 110,270,694,1870,5194,14786,42850,125934,374166,1121566,3386570,

%T 10289714,31434338,96493518,297491174,920787166,2860264522,8914266818,

%U 27866446818,87355159854,274542478518,864878298334,2730499054218

%N Number of (n+1) X (2+1) 0..3 arrays with every 2 X 2 subblock summing to 6 and no 2 X 2 subblock having exactly two nonzero entries.

%H R. H. Hardin, <a href="/A251230/b251230.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 11*a(n-1) - 42*a(n-2) + 49*a(n-3) + 69*a(n-4) - 184*a(n-5) + 18*a(n-6) + 160*a(n-7) - 32*a(n-8) - 48*a(n-9).

%F Empirical g.f.: 2*x*(55 - 470*x + 1172*x^2 + 93*x^3 - 3524*x^4 + 1898*x^5 + 3268*x^6 - 1352*x^7 - 1200*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 2*x - 4*x^2)). - _Colin Barker_, Nov 27 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 2 of A251236.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 30 2014

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)