A144560 Ten times hexagonal numbers: 10*n*(2*n-1).

0, 10, 60, 150, 280, 450, 660, 910, 1200, 1530, 1900, 2310, 2760, 3250, 3780, 4350, 4960, 5610, 6300, 7030, 7800, 8610, 9460, 10350, 11280, 12250, 13260, 14310, 15400, 16530, 17700, 18910, 20160, 21450, 22780, 24150, 25560, 27010

Offset: 0

Author

Omar E. Pol, Jan 01 2009

Keywords

• easy
• nonn

Comments

Sequence found by reading the line from 0, in the direction 0, 10,..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. - Omar E. Pol, Sep 18 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, A002939, A152745, A152994.

Programs

Magma

[10*n*(2*n-1): n in [0..40]]; // G. C. Greubel, May 30 2024

Mathematica

10*Binomial[2*Range[0,40], 2] (* G. C. Greubel, May 30 2024 *)

PARI

a(n)=10*n*(2*n-1) \\ Charles R Greathouse IV, Jun 17 2017

SageMath

[10*n*(2*n-1) for n in range(41)] # G. C. Greubel, May 30 2024

Formula

a(n) = 20*n^2 - 10*n = 10*A000384(n) = 5*A002939(n) = 2*A152745(n).

a(n) = a(n-1) +40*n -30 (with a(0)=0). - Vincenzo Librandi, Dec 14 2010

From G. C. Greubel, May 30 2024: (Start)

G.f.: 10*x*(1 + 3*x)/(1-x)^3.

E.g.f.: 10*x*(1 + 2*x)*exp(x). (End)