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Number of maximal independent sets in the 4 X n king graph.
2

%I #5 Feb 10 2020 21:47:53

%S 1,3,12,22,79,194,537,1519,4011,11258,30506,83661,229754,627171,

%T 1721547,4710045,12901630,35342272,96764537,265067580,725878627,

%U 1988023833,5444771405,14911382924,40839083772,111846316151,306317816028,838924085421,2297583803229,6292480053823

%N Number of maximal independent sets in the 4 X n king graph.

%H Andrew Howroyd, <a href="/A332349/b332349.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,3,-4,6,-3,-6).

%F a(n) = a(n-1) + 4*a(n-2) + 3*a(n-3) - 4*a(n-4) + 6*a(n-5) - 3*a(n-6) - 6*a(n-7) for n >= 7.

%F G.f.: (1 + 2*x + 5*x^2 - 5*x^3 + 4*x^4 - 3*x^5 - 6*x^6)/((1 - x)*(1 - 4*x^2 - 7*x^3 - 3*x^4 - 9*x^5 - 6*x^6)).

%o (PARI) Vec((1 + 2*x + 5*x^2 - 5*x^3 + 4*x^4 - 3*x^5 - 6*x^6)/((1 - x)*(1 - 4*x^2 - 7*x^3 - 3*x^4 - 9*x^5 - 6*x^6)) + O(x^40))

%Y Row n=4 of A332347.

%K nonn,easy

%O 0,2

%A _Andrew Howroyd_, Feb 10 2020