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 A152740 #46 Dec 27 2024 15:08:58
%S A152740 0,11,33,66,110,165,231,308,396,495,605,726,858,1001,1155,1320,1496,
%T A152740 1683,1881,2090,2310,2541,2783,3036,3300,3575,3861,4158,4466,4785,
%U A152740 5115,5456,5808,6171,6545,6930,7326,7733,8151,8580,9020,9471,9933,10406,10890,11385,11891
%N A152740 11 times triangular numbers.
%C A152740 Sequence found by reading the line from 0, in the direction 0, 11, ... and the same line from 0, in the direction 0, 33, ..., in the square spiral whose vertices are the generalized tridecagonal numbers A195313. Axis perpendicular to A195149 in the same spiral. - _Omar E. Pol_, Sep 18 2011
%C A152740 Sum of the numbers from 5*n to 6*n. - _Wesley Ivan Hurt_, Dec 22 2015
%H A152740 G. C. Greubel, <a href="/A152740/b152740.txt">Table of n, a(n) for n = 0..5000</a>
%H A152740 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A152740 a(n) = 11*n*(n+1)/2 = 11*A000217(n).
%F A152740 a(n) = a(n-1) + 11*n with n > 0, a(0)=0. - _Vincenzo Librandi_, Nov 26 2010
%F A152740 a(n) = A069125(n+1) - 1. - _Omar E. Pol_, Oct 03 2011
%F A152740 From _Philippe Deléham_, Mar 27 2013: (Start)
%F A152740 G.f.: 11*x/(1-x)^3.
%F A152740 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2, a(0)=0, a(1)=11, a(2)=33.
%F A152740 a(n) = A218530(11*n+10).
%F A152740 a(n) = A211013(n)+n = A022269(n)+5*n = A022268(n)+6*n = A180223(n)+9*n = A051865(n)+10*n. (End)
%F A152740 a(n) = Sum_{i=5*n..6*n} i. - _Wesley Ivan Hurt_, Dec 22 2015
%F A152740 From _Amiram Eldar_, Feb 21 2023: (Start)
%F A152740 Sum_{n>=1} 1/a(n) = 2/11.
%F A152740 Sum_{n>=1} (-1)^(n+1)/a(n) = (4*log(2) - 2)/11.
%F A152740 Product_{n>=1} (1 - 1/a(n)) = -(11/(2*Pi))*cos(sqrt(19/11)*Pi/2).
%F A152740 Product_{n>=1} (1 + 1/a(n)) = (11/(2*Pi))*cos(sqrt(3/11)*Pi/2). (End)
%F A152740 E.g.f.: 11*exp(x)*x*(2 + x)/2. - _Elmo R. Oliveira_, Dec 25 2024
%p A152740 A152740:=n->11*n*(n+1)/2: seq(A152740(n), n=0..60); # _Wesley Ivan Hurt_, Dec 22 2015
%t A152740 Table[11*n*(n - 1)/2, {n, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 06 2011 *)
%t A152740 LinearRecurrence[{3, -3, 1}, {0, 11, 33}, 100] (* _G. C. Greubel_, Dec 22 2015 *)
%o A152740 (Magma) [11*n*(n+1)/2 : n in [0..60]]; // _Wesley Ivan Hurt_, Dec 22 2015
%o A152740 (PARI) my(x='x+O('x^100)); concat(0, Vec(11*x/(1-x)^3)) \\ _Altug Alkan_, Dec 23 2015
%Y A152740 Cf. A000217, A022268, A022269, A049598, A051865, A069125, A124080, A180223, A195149, A195313, A211013, A218530.
%K A152740 nonn,easy
%O A152740 0,2
%A A152740 _Omar E. Pol_, Dec 12 2008