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 A049452 #54 Jul 03 2020 06:18:18
%S A049452 0,5,22,51,92,145,210,287,376,477,590,715,852,1001,1162,1335,1520,
%T A049452 1717,1926,2147,2380,2625,2882,3151,3432,3725,4030,4347,4676,5017,
%U A049452 5370,5735,6112,6501,6902,7315,7740,8177,8626,9087,9560,10045,10542
%N A049452 Pentagonal numbers with even index.
%C A049452 If Y is a 3-subset of an (2n+1)-set X then, for n>=4, a(n-1) is the number of 4-subsets of X having at least two elements in common with Y. - _Milan Janjic_, Dec 16 2007
%C A049452 Sequence found by reading the line (one of the diagonal axes) from 0, in the direction 0, 5,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - _Omar E. Pol_, Sep 08 2011
%C A049452 a(n) is the sum of 2*n consecutive integers starting from 2*n. - _Bruno Berselli_, Jan 16 2018
%H A049452 Harvey P. Dale, <a href="/A049452/b049452.txt">Table of n, a(n) for n = 0..1000</a>
%H A049452 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A049452 a(n) = n*(6*n-1).
%F A049452 G.f.: x*(5+7*x)/(1-x)^3.
%F A049452 a(n) = C(6*n,2)/3. - _Zerinvary Lajos_, Jan 02 2007
%F A049452 a(n) = A001105(n) + A033991(n) = A033428(n) + A049450(n) = A022266(n) + A000326(n). - _Zerinvary Lajos_, Jun 12 2007
%F A049452 a(n) = 12*n + a(n-1) - 7 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 06 2010
%F A049452 a(n) = 4*A000217(n) + A001107(n). - _Bruno Berselli_, Feb 11 2011
%F A049452 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2, a(0)=0, a(1)=5, a(2)=22. - _Harvey P. Dale_, Mar 07 2012
%F A049452 E.g.f.: (6*x^2 + 5*x)*exp(x). - _G. C. Greubel_, Jul 17 2017
%F A049452 From _Amiram Eldar_, Jul 03 2020: (Start)
%F A049452 Sum_{n>=1} 1/a(n) = 2*log(2) + 3*log(3)/2 - sqrt(3)*Pi/2.
%F A049452 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi - log(2) - 2*sqrt(3)*arccoth(sqrt(3)). (End)
%p A049452 seq(n*(6*n-1),n=0..42); # _Zerinvary Lajos_, Jun 12 2007
%t A049452 Table[n(6n-1),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,5,22},50] (* _Harvey P. Dale_, Mar 07 2012 *)
%o A049452 (PARI) a(n)=n*(6*n-1) \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A049452 Cf. A000326, A033570, A049453, A001318, A033568, A185019.
%Y A049452 See index to sequences with numbers of the form n*(d*n+10-d)/2 in A140090.
%K A049452 nonn,easy
%O A049452 0,2
%A A049452 Joe Keane (jgk(AT)jgk.org)