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a(n) = 2*n*(6*n-1).
2

%I #29 Sep 08 2022 08:45:29

%S 0,10,44,102,184,290,420,574,752,954,1180,1430,1704,2002,2324,2670,

%T 3040,3434,3852,4294,4760,5250,5764,6302,6864,7450,8060,8694,9352,

%U 10034,10740,11470,12224,13002,13804,14630,15480,16354,17252,18174,19120,20090,21084

%N a(n) = 2*n*(6*n-1).

%D V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.

%H G. C. Greubel, <a href="/A126964/b126964.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) = 24*n + a(n-1) - 14 for n>0, a(0)=0. - _Vincenzo Librandi_, Nov 23 2010

%F From _Harvey P. Dale_, Nov 19 2011: (Start)

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2, a(0)=0, a(1)=10, a(2)=44.

%F G.f.: (10*x + 14*x^2)/(1 - x)^3. (End)

%F From _Ilya Gutkovskiy_, Dec 04 2016: (Start)

%F Sum_{n>=1} 1/a(n) = (4*log(2) + 3*log(3) - sqrt(3)*Pi)/4 = 0.15675687388...

%F E.g.f.: 2*x*(5 + 6*x)*exp(x). (End)

%F a(n) = Sum_{i=n..5*n-1} i. - _Wesley Ivan Hurt_, Dec 04 2016

%p A126964:=n->2*n*(6*n-1): seq(A126964(n), n=0..60); # _Wesley Ivan Hurt_, Dec 03 2016

%t Table[2n(6n-1),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,10,44},50] (* _Harvey P. Dale_, Nov 19 2011 *)

%o (Magma) [2*n*(6*n-1) : n in [0..50]]; // _Wesley Ivan Hurt_, Dec 03 2016

%o (PARI) a(n)=2*n*(6*n-1) \\ _Charles R Greathouse IV_, Jun 16 2017

%o (Sage) [2*binomial(6*n,2)/3 for n in (0..50)] # _G. C. Greubel_, Jan 29 2020

%o (GAP) List([0..50], n-> 2*Binomial(6*n,2)/3 ); # _G. C. Greubel_, Jan 29 2020

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Mar 21 2007