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A202804 a(n) = n*(6*n+4). 4

%I

%S 0,10,32,66,112,170,240,322,416,522,640,770,912,1066,1232,1410,1600,

%T 1802,2016,2242,2480,2730,2992,3266,3552,3850,4160,4482,4816,5162,

%U 5520,5890,6272,6666,7072,7490,7920,8362,8816,9282,9760,10250,10752,11266,11792

%N a(n) = n*(6*n+4).

%C Sequence found by reading the line from 0, in the direction 0, 10,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. Opposite numbers to the members of A033579 in the same spiral. - _Omar E. Pol_, Jul 17 2012

%H Jeremy Gardiner, <a href="/A202804/b202804.txt">Table of n, a(n) for n = 0..3000</a>

%H M. Janjic and B. Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv 1301.4550 [math.CO], 2013.

%H P. Vavolas, <a href="http://www.dcs.shef.ac.uk/intranet/teaching/projects/archive/msc2005/pdf/m4pv.pdf">Cellular automaton model of cardiac arrhythmias</a>, University of Sheffield Department of Computer Science (2005), (see page 43).

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

%F a(n) = 2*n(3n+2) = 6n^2 + 4n = 2*A045944.

%F a(n) = A080859(n) - 1. - _Omar E. Pol_, Jul 18 2012

%F a(0)=0, a(1)=10, a(2)=32, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - _Harvey P. Dale_, Dec 28 2015

%F G.f.: -2x(5 + x)/(x - 1)^3. - _Indranil Ghosh_, Apr 10 2017

%p A202804:=n->n*(6*n+4): seq(A202804(n), n=0..100); # _Wesley Ivan Hurt_, Apr 09 2017

%t Table[n(6n+4),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,10,32},50] (* _Harvey P. Dale_, Dec 28 2015 *)

%o (PARI) x='x + O('x^50); concat([0], Vec(-2*x*(5 + x)/(x - 1)^3)) \\ _Indranil Ghosh_, Apr 10 2017

%Y Cf. A033581, A049453, A033580, A195319.

%K nonn,easy

%O 0,2

%A _Jeremy Gardiner_, Dec 24 2011

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Last modified September 22 12:42 EDT 2019. Contains 327307 sequences. (Running on oeis4.)