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 A211014 Second 14-gonal numbers: n*(6*n+5). 5
 0, 11, 34, 69, 116, 175, 246, 329, 424, 531, 650, 781, 924, 1079, 1246, 1425, 1616, 1819, 2034, 2261, 2500, 2751, 3014, 3289, 3576, 3875, 4186, 4509, 4844, 5191, 5550, 5921, 6304, 6699, 7106, 7525, 7956, 8399, 8854, 9321, 9800, 10291, 10794 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence found by reading the line from 0, in the direction 0, 34... and the line from 11 in the direction 11, 69,..., in the square spiral whose vertices are the generalized 14-gonal numbers A195818. LINKS Ivan Panchenko, Table of n, a(n) for n = 0..1000 Mark W. Coffey, Bernoulli identities, zeta relations, determinant expressions, Mellin transforms, and representation of the Hurwitz numbers, arXiv:1601.01673 [math.NT], 2016. See 3rd formula in Proposition 3 p. 36 giving a(n+1). Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = -2*Sum_{k=0..n-1} binomial(6*n+5, 6*k+8)*bernoulli(6*k+8)). - Michel Marcus, Jan 11 2016 From G. C. Greubel, Jul 04 2019: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). G.f.: x*(11+x)/(1-x)^3. E.g.f.: x*(11+6*x)*exp(x). (End) MATHEMATICA Table[n*(6*n+5), {n, 0, 50}] (* G. C. Greubel, Jul 04 2019 *) PROG (PARI) a(n)=n*(6*n+5) \\ Charles R Greathouse IV, Jun 17 2017 (MAGMA) [n*(6*n+5): n in [0..50]]; // G. C. Greubel, Jul 04 2019 (Sage) [n*(6*n+5) for n in (0..50)] # G. C. Greubel, Jul 04 2019 (GAP) List([0..50], n-> n*(6*n+5)) # G. C. Greubel, Jul 04 2019 CROSSREFS Bisection of A195818. Second k-gonal numbers (k=5..14): A005449, A014105, A147875, A045944, A179986, A033954, A062728, A135705, A211013, this sequence. Cf. A051866. Sequence in context: A226502 A041230 A063162 * A103661 A300418 A041539 Adjacent sequences:  A211011 A211012 A211013 * A211015 A211016 A211017 KEYWORD nonn,easy AUTHOR Omar E. Pol, Aug 04 2012 STATUS approved

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Last modified August 17 17:25 EDT 2019. Contains 326059 sequences. (Running on oeis4.)