A144560 - OEIS

%I #21 May 30 2024 06:57:00

%S 0,10,60,150,280,450,660,910,1200,1530,1900,2310,2760,3250,3780,4350,

%T 4960,5610,6300,7030,7800,8610,9460,10350,11280,12250,13260,14310,

%U 15400,16530,17700,18910,20160,21450,22780,24150,25560,27010

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

%C 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

%H Ivan Panchenko, <a href="/A144560/b144560.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

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

%F a(n) = a(n-1) +40*n -30  (with a(0)=0). - _Vincenzo Librandi_, Dec 14 2010

%F From _G. C. Greubel_, May 30 2024: (Start)

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

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

%t 10*Binomial[2*Range[0,40], 2] (* _G. C. Greubel_, May 30 2024 *)

%o (PARI) a(n)=10*n*(2*n-1) \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Magma) [10*n*(2*n-1): n in [0..40]]; // _G. C. Greubel_, May 30 2024

%o (SageMath) [10*n*(2*n-1) for n in range(41)] # _G. C. Greubel_, May 30 2024

%Y Cf. A000384, A002939, A152745, A152994.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, Jan 01 2009