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 A152746 Six times hexagonal numbers: 6*n*(2*n-1). 14
 0, 6, 36, 90, 168, 270, 396, 546, 720, 918, 1140, 1386, 1656, 1950, 2268, 2610, 2976, 3366, 3780, 4218, 4680, 5166, 5676, 6210, 6768, 7350, 7956, 8586, 9240, 9918, 10620, 11346, 12096, 12870, 13668, 14490, 15336, 16206, 17100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence found by reading the line from 0, in the direction 0, 6, ..., in the square spiral whose vertices are the generalized octagonal numbers A001082. - Omar E. Pol, Sep 18 2011 a(n) is the number of walks on a cubic lattice of n dimensions that return to the origin, not necessarily for the first time, after 4 steps. - Shel Kaphan, Mar 20 2023 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) = 12*n^2 - 6*n = A000384(n)*6 = A002939(n)*3 = A094159(n)*2. a(n) = a(n-1) + 24*n - 18 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010 From G. C. Greubel, Sep 01 2018: (Start) G.f.: 6*x*(1+3*x)/(1-x)^3. E.g.f.: 6*x*(1+2*x)*exp(x). (End) From Amiram Eldar, Mar 30 2023: (Start) Sum_{n>=1} 1/a(n) = log(2)/3. Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/12 - log(2)/6. (End) MATHEMATICA 6*PolygonalNumber[6, Range[0, 40]] (* The program uses the PolygonalNumber function from Mathematica version 10 *) (* Harvey P. Dale, Mar 04 2016 *) LinearRecurrence[{3, -3, 1}, {0, 6, 36}, 50] (* or *) Table[6*n*(2*n-1), {n, 0, 50}] (* G. C. Greubel, Sep 01 2018 *) PROG (PARI) a(n)=6*n*(2*n-1) \\ Charles R Greathouse IV, Jun 17 2017 (Magma) [6*n*(2*n-1): n in [0..50]]; // G. C. Greubel, Sep 01 2018 CROSSREFS Cf. A000384, A001082, A002939, A094159, A085250, A152745. Column n=2 of A287318. Sequence in context: A207896 A207656 A207341 * A207363 A207600 A207026 Adjacent sequences: A152743 A152744 A152745 * A152747 A152748 A152749 KEYWORD easy,nonn,walk AUTHOR Omar E. Pol, Dec 12 2008 STATUS approved

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Last modified December 8 14:30 EST 2023. Contains 367679 sequences. (Running on oeis4.)