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 A317974 a(n) = 2*(a(n-1)+a(n-2)+a(n-3))-a(n-4) for n >= 4, with initial terms 0,0,1,1. 4
 0, 0, 1, 1, 4, 12, 33, 97, 280, 808, 2337, 6753, 19516, 56404, 163009, 471105, 1361520, 3934864, 11371969, 32865601, 94983348, 274506972, 793339873, 2292794785, 6626299912, 19150362168, 55345573857, 159951677089, 462268926316, 1335981992356, 3861059617665 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS A.H.M. Smeets, Table of n, a(n) for n = 0..2172 H. S. M. Coxeter, Loxodromic sequences of tangent spheres, Aequationes Mathematicae, 1.1-2 (1968): 104-121. See p. 112. Eric Weisstein's World of Mathematics, Coxeter's Loxodromic Sequence of Tangent Circles Index entries for linear recurrences with constant coefficients, signature (2,2,2,-1). FORMULA Lim {n -> infinity} log(a(n))/n = 1.0612750619050... = log(phi+sqrt(phi)) = log(A001622+A139339), where phi is the golden ratio. - A.H.M. Smeets, Sep 04 2018 G.f.: x^2*(1 - x) / (1 - 2*x - 2*x^2 - 2*x^3 + x^4). - Colin Barker, Sep 04 2018 PROG (Python) a1, a2, a3, a4, n = 1, 1, 0, 0, 3 print(0, 0) print(1, 0) print(2, 1) print(3, 1) while n < 2172: ....a1, a2, a3, a4, n = 2*(a1+a2+a3)-a4, a1, a2, a3, n+1 ....print(n, a1) # A.H.M. Smeets, Sep 04 2018 (PARI) concat(vector(2), Vec(x^2*(1 - x) / (1 - 2*x - 2*x^2 - 2*x^3 + x^4) + O(x^40))) \\ Colin Barker, Sep 04 2018 CROSSREFS Sequence in context: A135254 A326804 A000754 * A119683 A331834 A135373 Adjacent sequences:  A317971 A317972 A317973 * A317975 A317976 A317977 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Sep 03 2018 STATUS approved

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Last modified August 8 08:27 EDT 2020. Contains 336293 sequences. (Running on oeis4.)