A152745 5 times hexagonal numbers: 5*n*(2*n-1).

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

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