Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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