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 A144537 a(0) = 3; for n > 0, a(n) = sqrt(3)*(P^(2*n)-M^(2*n))/8 + (3/4)*(P^n+M^n) + 1/2), where P = 7+4*sqrt(3), M = 7-4*sqrt(3). 0

%I

%S 3,53,8294,1582697,306670058,59487327869,11540164172942,

%T 2238731376614513,434302333171290194,84252413712650759237,

%U 16344533955257962820918,3170755334869239754891769,615110190430160624256865082,119328206188109096135248101773,23149056890302634266012500544094

%N a(0) = 3; for n > 0, a(n) = sqrt(3)*(P^(2*n)-M^(2*n))/8 + (3/4)*(P^n+M^n) + 1/2), where P = 7+4*sqrt(3), M = 7-4*sqrt(3).

%C Arises in studying a certain sequence of two-dimensional lattices.

%D Reference will added later.

%F a(n)= +209*a(n-1) -2926*a(n-2) +2926*a(n-3) -209*a(n-4) +a(n-5), n>5. G.f.: (574*x-5995*x^2+4449*x^3-178*x^4+x^5-3)/((x-1) * (x^2-14*x+1) * (x^2-194*x+1)). [From _R. J. Mathar_, Jul 26 2010]

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Dec 29 2008

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Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)