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 A033580 Four times second pentagonal numbers: a(n) = 2*n*(3*n+1). 12
 0, 8, 28, 60, 104, 160, 228, 308, 400, 504, 620, 748, 888, 1040, 1204, 1380, 1568, 1768, 1980, 2204, 2440, 2688, 2948, 3220, 3504, 3800, 4108, 4428, 4760, 5104, 5460, 5828, 6208, 6600, 7004, 7420, 7848, 8288, 8740, 9204, 9680, 10168, 10668, 11180, 11704, 12240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Subsequence of A062717: A010052(6*a(n)+1) = 1. - Reinhard Zumkeller, Feb 21 2011 Sequence found by reading the line from 0, in the direction 0, 8,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. Opposite numbers to the members of A139267 in the same spiral - Omar E. Pol, Sep 09 2011 a(n) is the number of edges of the octagonal network O(n,n); O(m,n) is defined by Fig. 1 of the Siddiqui et al. reference. - Emeric Deutsch May 13 2018 REFERENCES M. K. Siddiqui, M. Naeem, N. A. Rahman, and M. Imran, Computing topological indices of  certain networks, J. of Optoelectronics and Advanced Materials , 18, No. 9-10, 2016, 884-892. LINKS Ivan Panchenko, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = a(n-1) +12*n -4 (with a(0)=0). - Vincenzo Librandi, Aug 05 2010 G.f.: 4*x*(2+x)/(1-x)^3. - Colin Barker, Feb 13 2012 a(-n) = A033579(n). - Michael Somos, Jun 09 2014 E.g.f.: 2*x*(4 + 3*x)*exp(x). - G. C. Greubel, Oct 09 2019 MAPLE seq(2*n*(3*n+1), n=0..50); # G. C. Greubel, Oct 09 2019 MATHEMATICA 4*Binomial[3*Range-2, 2]/3 (* G. C. Greubel, Oct 09 2019 *) PROG (PARI) a(n)=2*n*(3*n+1) \\ Charles R Greathouse IV, Sep 28 2015 (MAGMA) [2*n*(3*n+1): n in [0..50]]; // G. C. Greubel, Oct 09 2019 (Sage) [2*n*(3*n+1) for n in (0..50)] # G. C. Greubel, Oct 09 2019 (GAP) List([0..50], n-> 2*n*(3*n+1)); # G. C. Greubel, Oct 09 2019 CROSSREFS Cf. A033579, A049451, A045945, A186423. Cf. sequences listed in A254963. Sequence in context: A173681 A045850 A264354 * A299289 A212515 A007331 Adjacent sequences:  A033577 A033578 A033579 * A033581 A033582 A033583 KEYWORD nonn,easy,changed AUTHOR STATUS approved

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Last modified October 16 11:06 EDT 2019. Contains 328056 sequences. (Running on oeis4.)