A144537 - OEIS

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).

3, 53, 8294, 1582697, 306670058, 59487327869, 11540164172942, 2238731376614513, 434302333171290194, 84252413712650759237, 16344533955257962820918, 3170755334869239754891769, 615110190430160624256865082, 119328206188109096135248101773, 23149056890302634266012500544094

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OFFSET

0,1

COMMENTS

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

REFERENCES

Reference will added later.

LINKS

Table of n, a(n) for n=0..14.

FORMULA

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]

CROSSREFS

Sequence in context: A118194 A325725 A173357 * A208631 A093164 A092448

Adjacent sequences: A144534 A144535 A144536 * A144538 A144539 A144540

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 29 2008

STATUS

approved