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.
%I A135706 #53 May 09 2025 19:52:25
%S A135706 0,2,14,36,68,110,162,224,296,378,470,572,684,806,938,1080,1232,1394,
%T A135706 1566,1748,1940,2142,2354,2576,2808,3050,3302,3564,3836,4118,4410,
%U A135706 4712,5024,5346,5678,6020,6372,6734,7106,7488,7880,8282,8694,9116,9548,9990,10442
%N A135706 a(n) = n*(5*n-3).
%C A135706 Twice heptagonal numbers. - _Omar E. Pol_, May 14 2008
%H A135706 G. C. Greubel, <a href="/A135706/b135706.txt">Table of n, a(n) for n = 0..1000</a>
%H A135706 Lancelot 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 A135706 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A135706 Binomial transform of [2, 12, 10, 0, 0, 0, ...]. - _Gary W. Adamson_, Mar 05 2008
%F A135706 a(n) = 2*A000566(n). - _Omar E. Pol_, May 14 2008
%F A135706 a(n) = a(n-1) + 10*n - 8 (with a(0)=0). - _Vincenzo Librandi_, Nov 24 2010
%F A135706 a(n) = A131242(10n+1). - _Philippe Deléham_, Mar 27 2013
%F A135706 From _G. C. Greubel_, Oct 29 2016: (Start)
%F A135706 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A135706 G.f.: 2*x*(1 + 4*x)/(1 - x)^3.
%F A135706 E.g.f.: x*(2 + 5*x)*exp(x). (End)
%F A135706 Sum_{n>=1} 1/a(n) = tan(Pi/10)*Pi/6 - sqrt(5)*log(phi)/6 + 5*log(5)/12, where phi is the golden ratio (A001622). - _Amiram Eldar_, Jul 19 2022
%t A135706 LinearRecurrence[{3,-3,1}, {0,2,14}, 50] (* or *) Table[n*(5*n-3), {n, 0, 50}] (* _G. C. Greubel_, Oct 29 2016 *)
%o A135706 (PARI) a(n)=n*(5*n-3) \\ _Charles R Greathouse IV_, Oct 07 2015
%o A135706 (Magma) [n*(5*n-3): n in [0..50]]; // _G. C. Greubel_, Jul 05 2019
%o A135706 (Sage) [n*(5*n-3) for n in (0..50)] # _G. C. Greubel_, Jul 05 2019
%o A135706 (GAP) List([0..50], n-> n*(5*n-3)); # _G. C. Greubel_, Jul 05 2019
%Y A135706 Cf. A000566, A001622, A131242.
%Y A135706 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 A135706 nonn,easy
%O A135706 0,2
%A A135706 _N. J. A. Sloane_, Mar 04 2008, Mar 05 2008