cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A144560 #21 May 30 2024 06:57:00
%S A144560 0,10,60,150,280,450,660,910,1200,1530,1900,2310,2760,3250,3780,4350,
%T A144560 4960,5610,6300,7030,7800,8610,9460,10350,11280,12250,13260,14310,
%U A144560 15400,16530,17700,18910,20160,21450,22780,24150,25560,27010
%N A144560 Ten times hexagonal numbers: 10*n*(2*n-1).
%C A144560 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 A144560 Ivan Panchenko, <a href="/A144560/b144560.txt">Table of n, a(n) for n = 0..1000</a>
%H A144560 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A144560 a(n) = 20*n^2 - 10*n = 10*A000384(n) = 5*A002939(n) = 2*A152745(n).
%F A144560 a(n) = a(n-1) +40*n -30  (with a(0)=0). - _Vincenzo Librandi_, Dec 14 2010
%F A144560 From _G. C. Greubel_, May 30 2024: (Start)
%F A144560 G.f.: 10*x*(1 + 3*x)/(1-x)^3.
%F A144560 E.g.f.: 10*x*(1 + 2*x)*exp(x). (End)
%t A144560 10*Binomial[2*Range[0,40], 2] (* _G. C. Greubel_, May 30 2024 *)
%o A144560 (PARI) a(n)=10*n*(2*n-1) \\ _Charles R Greathouse IV_, Jun 17 2017
%o A144560 (Magma) [10*n*(2*n-1): n in [0..40]]; // _G. C. Greubel_, May 30 2024
%o A144560 (SageMath) [10*n*(2*n-1) for n in range(41)] # _G. C. Greubel_, May 30 2024
%Y A144560 Cf. A000384, A002939, A152745, A152994.
%K A144560 easy,nonn
%O A144560 0,2
%A A144560 _Omar E. Pol_, Jan 01 2009