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 A152745 5 times hexagonal numbers: 5*n*(2*n-1). 5
 0, 5, 30, 75, 140, 225, 330, 455, 600, 765, 950, 1155, 1380, 1625, 1890, 2175, 2480, 2805, 3150, 3515, 3900, 4305, 4730, 5175, 5640, 6125, 6630, 7155, 7700, 8265, 8850, 9455, 10080, 10725, 11390, 12075, 12780, 13505, 14250, 15015 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence found by reading the line from 0, in the direction 0, 5, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Sep 18 2011 Also sequence found by reading the line from 0, in the direction 0, 5, ..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. This is one of the four semi-diagonals of the spiral. - Omar E. Pol, Oct 14 2011 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) = 10*n^2 - 5*n = A000384(n)*5. a(n) = a(n-1) + 20*n-15 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010 From G. C. Greubel, Sep 01 2018: (Start) G.f.: 5*x*(1+ 3*x)/(1-x)^3. E.g.f.: 5*x*(1+2*x)*exp(x). (End) From Vaclav Kotesovec, Sep 02 2018: (Start) Sum_{n>=1} 1/a(n) = 2*log(2)/5. Sum_{n>=1} (-1)^n/a(n) = log(2)/5 - Pi/10. (End) MATHEMATICA LinearRecurrence[{3, -3, 1}, {0, 5, 30}, 50] (* or *) Table[5*n*(2*n-1), {n, 0, 50}] (* G. C. Greubel, Sep 01 2018 *) PROG (PARI) a(n)=5*n*(2*n-1) \\ Charles R Greathouse IV, Jun 17 2017 (Magma) [5*n*(2*n-1): n in [0..50]]; // G. C. Greubel, Sep 01 2018 CROSSREFS Cf. A000384, A085250, A152746. Bisection of A028895. Sequence in context: A044463 A270811 A331507 * A187275 A344070 A273480 Adjacent sequences:  A152742 A152743 A152744 * A152746 A152747 A152748 KEYWORD easy,nonn AUTHOR Omar E. Pol, Dec 12 2008 STATUS approved

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Last modified September 27 19:37 EDT 2022. Contains 357063 sequences. (Running on oeis4.)