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A298141 Number of n X 3 0..1 arrays with every element equal to 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero. 2

%I #8 Mar 22 2018 17:08:01

%S 0,2,0,2,1,6,8,15,22,44,82,152,267,486,898,1675,3088,5686,10512,19530,

%T 36309,67442,125268,232951,433598,807304,1503082,2798968,5213647,

%U 9713698,18099774,33727651,62853728,117142090,218334832,406958706,758560313

%N Number of n X 3 0..1 arrays with every element equal to 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Column 3 of A298146.

%H R. H. Hardin, <a href="/A298141/b298141.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 2*a(n-2) + 2*a(n-5) - 4*a(n-6) - 8*a(n-7) - a(n-8) + a(n-9).

%F Empirical g.f.: x^2*(1 - x)*(2 - 2*x^2 - 3*x^3 - 2*x^4 - 6*x^5 - 3*x^6) / ((1 + x)*(1 - 2*x - 2*x^5 + 6*x^6 + 2*x^7 - x^8)). - _Colin Barker_, Mar 22 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Cf. A298146.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 13 2018

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)