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 A030511 Graham-Sloane-type lower bound on the size of a ternary (n,3,3) constant-weight code. 13
 2, 6, 10, 16, 24, 32, 42, 54, 66, 80, 96, 112, 130, 150, 170, 192, 216, 240, 266, 294, 322, 352, 384, 416, 450, 486, 522, 560, 600, 640, 682, 726, 770, 816, 864, 912, 962, 1014, 1066, 1120, 1176, 1232, 1290, 1350, 1410, 1472, 1536, 1600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS With a different offset this is the elliptic troublemaker sequence R_n(2,6) (also sequence R_n(4,6)) in the notation of Stange (see Table 1, p.16). For other elliptic troublemaker sequences R_n(a,b) see the cross references below. - Peter Bala, Aug 12 2013 LINKS Craig Knecht, Maximum number of enneiamonds in a hexagon. K. E. Stange, Integral points on elliptic curves and explicit valuations of division polynomials arXiv:1108.3051 [math.NT], 2011-2014. M. Svanstrom, A lower bound for ternary constant weight codes, IEEE Trans. on Information Theory, Vol. 43, pp. 1630-1632, Sep. 1997. Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1). FORMULA a(n) = 2 * (n - 1)^2 / 3 if n==1 (mod 3), a(n) = 2 * n * (n - 2) / 3 otherwise. G.f.: -2*x^3*(1 + x) / ( (1 + x + x^2)*(x - 1)^3 ). - R. J. Mathar, Aug 25 2011 a(n) = 2*A000212(n-1). - R. J. Mathar, Aug 25 2011 a(n) = floor( (2/3)*(n-1)^2 ). - Wesley Ivan Hurt, Jun 19 2013 a(n) = (2*(n - 2)*n - (-1)^floor(2*(n-2)/3) + 1)/3. - Bruno Berselli, Aug 08 2013 a(n) = a(n-1) + 2*floor((n-1)*2/3). - Gionata Neri, Apr 26 2015 a(n) = floor((n-2)*(n-1)/3) + floor((n-1)*n/3) = floor((n-1)*(n+1)/3) + floor((n-1)*(n-3)/3). - Bruno Berselli, Mar 02 2017 MATHEMATICA LinearRecurrence[{2, -1, 1, -2, 1}, {2, 6, 10, 16, 24}, 50] (* Harvey P. Dale, Mar 03 2016 *) CROSSREFS Elliptic troublemaker sequences: A000212 (= R_n(1,3) = R_n(2,3)), A002620 (= R_n(1,2)), A007590 (= R_n(2,4)), A033436 (= R_n(1,4) = R_n(3,4)), A033437 (= R_n(1,5) = R_n(4,5)), A033438 (= R_n(1,6) = R_n(5,6)), A033439 (= R_n(1,7) = R_n(6,7)), A184535 (= R_n(2,5) = R_n(3,5)). Sequence in context: A183575 A096184 A254829 * A071597 A100899 A099540 Adjacent sequences:  A030508 A030509 A030510 * A030512 A030513 A030514 KEYWORD nonn,easy AUTHOR Mattias Svanstrom (mattias(AT)isy.liu.se) STATUS approved

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Last modified October 22 19:53 EDT 2019. Contains 328319 sequences. (Running on oeis4.)