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 A033587 a(n) = 2*n*(4*n + 3). 11
 0, 14, 44, 90, 152, 230, 324, 434, 560, 702, 860, 1034, 1224, 1430, 1652, 1890, 2144, 2414, 2700, 3002, 3320, 3654, 4004, 4370, 4752, 5150, 5564, 5994, 6440, 6902, 7380, 7874, 8384, 8910, 9452, 10010, 10584, 11174, 11780, 12402, 13040, 13694, 14364, 15050 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The inverse binomial transform is [0, 14, 16, 0, 0, 0, ...]. - R. J. Mathar, May 06 2008 Sequence found by reading the line from 0, in the direction 0, 14, ..., in the square spiral whose vertices are the triangular numbers A000217. Opposite numbers to the even hexagonal numbers A014635 in the same spiral. - Omar E. Pol, Sep 03 2011 LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 2*A033954(n). O.g.f.: 2*x*(7+x)/(1-x)^3. - R. J. Mathar, May 06 2008 a(n) = 16*n + a(n-1) - 2 with a(0)=0. - Vincenzo Librandi, Aug 05 2010 E.g.f.: (8*x^2 + 14*x)*exp(x). - G. C. Greubel, Jul 18 2017 From Vaclav Kotesovec, Aug 18 2018: (Start) Sum_{n>=1} 1/a(n) = 2/9 + Pi/12 - log(2)/2. Sum_{n>=1} (-1)^n/a(n) = 2/9 - Pi/(6*sqrt(2)) - log(2)/6 + log(1+sqrt(2))/(3*sqrt(2)). (End) MATHEMATICA Table[2*n(4*n + 3), {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *) LinearRecurrence[{3, -3, 1}, {0, 14, 44}, 80] (* Harvey P. Dale, Jun 05 2019 *) PROG (PARI) a(n)=2*n*(4*n+3) \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Sequence in context: A064125 A089031 A265152 * A189807 A009942 A031130 Adjacent sequences: A033584 A033585 A033586 * A033588 A033589 A033590 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified May 18 11:53 EDT 2024. Contains 372630 sequences. (Running on oeis4.)