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A135706 a(n) = n*(5*n-3). 11

%I

%S 0,2,14,36,68,110,162,224,296,378,470,572,684,806,938,1080,1232,1394,

%T 1566,1748,1940,2142,2354,2576,2808,3050,3302,3564,3836,4118,4410,

%U 4712,5024,5346,5678,6020,6372,6734,7106,7488,7880,8282,8694,9116,9548,9990,10442

%N a(n) = n*(5*n-3).

%C Twice heptagonal numbers. - _Omar E. Pol_, May 14 2008

%H G. C. Greubel, <a href="/A135706/b135706.txt">Table of n, a(n) for n = 0..1000</a>

%H L. Hogben, <a href="https://archive.org/details/chanceandchoiceb029729mbp/page/n39">Choice and Chance by Cardpack and Chessboard</a>, Vol. 1, Max Parrish and Co, London, 1950, p. 36.

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

%F Binomial transform of [2, 12, 10, 0, 0, 0,...]. - _Gary W. Adamson_, Mar 05 2008

%F a(n) = 2*A000566(n). - _Omar E. Pol_, May 14 2008

%F a(n) = a(n-1) + 10*n - 8 (with a(0)=0). - _Vincenzo Librandi_, Nov 24 2010

%F a(n) = A131242(10n+1). - _Philippe Deléham_, Mar 27 2013

%F From _G. C. Greubel_, Oct 29 2016: (Start)

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

%F G.f.: 2*x*(1 + 4*x)/(1 - x)^3.

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

%t LinearRecurrence[{3,-3,1}, {0,2,14}, 50] (* or *) Table[n*(5*n-3), {n, 0, 50}] (* _G. C. Greubel_, Oct 29 2016 *)

%o (PARI) a(n)=n*(5*n-3) \\ _Charles R Greathouse IV_, Oct 07 2015

%o (MAGMA) [n*(5*n-3): n in [0..50]]; // _G. C. Greubel_, Jul 05 2019

%o (Sage) [n*(5*n-3) for n in (0..50)] # _G. C. Greubel_, Jul 05 2019

%o (GAP) List([0..50], n-> n*(5*n-3)) # _G. C. Greubel_, Jul 05 2019

%Y Cf. A000566.

%Y Cf. numbers of the form n*(n*k-k+4))/2 listed in A226488 (this sequence is the case k=10). - _Bruno Berselli_, Jun 10 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Mar 04 2008, Mar 05 2008

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Last modified September 17 12:57 EDT 2019. Contains 327131 sequences. (Running on oeis4.)