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

Author

Omar E. Pol, Dec 12 2008

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A000384, A085250, A152746.

Bisection of A028895.

Programs

Magma

[5*n*(2*n-1): n in [0..50]]; // G. C. Greubel, Sep 01 2018

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 *)

PARI

a(n)=5*n*(2*n-1) \\ Charles R Greathouse IV, Jun 17 2017

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)