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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
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
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
Bisection of A028895.
Sequence in context: A044463 A270811 A331507 * A187275 A344070 A273480
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Dec 12 2008
STATUS
approved