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 A094159 3 times hexagonal numbers: a(n) = 3*n*(2*n-1). 25
 0, 3, 18, 45, 84, 135, 198, 273, 360, 459, 570, 693, 828, 975, 1134, 1305, 1488, 1683, 1890, 2109, 2340, 2583, 2838, 3105, 3384, 3675, 3978, 4293, 4620, 4959, 5310, 5673, 6048, 6435, 6834, 7245, 7668, 8103, 8550, 9009, 9480, 9963, 10458, 10965, 11484 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Column 3 of A048790. Sequence found by reading the line from 0, in the direction 0, 3, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Sep 08 2011 a(n) is the sum of all perimeters of triangles having two sides of length n. For n=4 one has seven triangles with two sides of length 4 and the other of lengths 1..7. - J. M. Bergot, Mar 26 2014 a(n) is the Wiener index of the complete tripartite graph K_{n,n,n}. - Eric W. Weisstein, Sep 07 2017 Sequence found by reading the line from 0, in the direction 0, 3, ..., in a spiral on an equilateral triangular lattice. - Hans G. Oberlack, Dec 08 2018 REFERENCES Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Hans G. Oberlack, Triangle spiral R. C. Schroeppel, A few mathematical experiments. Eric Weisstein's World of Mathematics, Complete Tripartite Graph Eric Weisstein's World of Mathematics, Wiener Index Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 6*n^2 - 3*n = 3*n*(2*n-1) = 3*A000384(n). - Omar E. Pol, Dec 11 2008 a(n) = 12*n + a(n-1) - 9 with n > 0, a(0)=0. - Vincenzo Librandi, Nov 16 2010 G.f.: 3*x*(1+3*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011 Sum_{n>0} 1/a(n) = (2/3)*log(2). - Enrique Pérez Herrero, Jun 04 2015 E.g.f.: 3*x*(1+2*x)*exp(x). - G. C. Greubel, Dec 07 2018 MAPLE A094159:=n->3*n*(2*n-1); seq(A094159(n), n=0..40); # Wesley Ivan Hurt, Mar 28 2014 MATHEMATICA CoefficientList[Series[3x(1+3x)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 19 2013 *) Table[3n(2n-1), {n, 0, 50}] (* or *) 3*PolygonalNumber[6, Range[0, 50]] (* or *) LinearRecurrence[{3, -3, 1}, {3, 18, 45}, {0, 50}] (* Eric W. Weisstein, Sep 07 2017 *) PROG (PARI) a(n)=3*n*(2*n-1) \\ Charles R Greathouse IV, Sep 24 2015 (MAGMA) [3*n*(2*n-1): n in [0..50]]; // G. C. Greubel, Dec 07 2018 (Sage) [3*n*(2*n-1) for n in range(50)] # G. C. Greubel, Dec 07 2018 (GAP) List([0..50], n -> 3*n*(2*n-1)); # G. C. Greubel, Dec 07 2018 CROSSREFS Cf. A000384, A048790. 3 times n-gonal numbers: A045943, A033428, A062741, A152773, A152751, A152759, A152767, A153783, A153448, A153875. Essentially a bisection of A045943. - Omar E. Pol, Sep 17 2011 Cf. numbers of the form n*(n*k-k+6))/2, this sequence is the case k=12: see Comments lines of A226492. Sequence in context: A097989 A039700 A069147 * A138976 A275038 A304976 Adjacent sequences:  A094156 A094157 A094158 * A094160 A094161 A094162 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, May 05 2004 EXTENSIONS More terms from Vladimir Joseph Stephan Orlovsky, Nov 16 2008 Definition improved, offset corrected and edited by Omar E. Pol, Dec 11 2008 STATUS approved

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Last modified May 25 19:11 EDT 2019. Contains 323576 sequences. (Running on oeis4.)