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 A049453 #46 Dec 12 2024 17:16:38
%S A049453 0,7,26,57,100,155,222,301,392,495,610,737,876,1027,1190,1365,1552,
%T A049453 1751,1962,2185,2420,2667,2926,3197,3480,3775,4082,4401,4732,5075,
%U A049453 5430,5797,6176,6567,6970,7385,7812,8251,8702,9165,9640,10127,10626,11137,11660,12195
%N A049453 Second pentagonal numbers with even index: a(n) = n*(6*n+1).
%C A049453 Number of edges in the join of the complete tripartite graph of order 3n and the cycle graph of order n, K_n,n,n * C_n. - _Roberto E. Martinez II_, Jan 07 2002
%C A049453 Sequence found by reading the line (one of the diagonal axes) from 0, in the direction 0, 7, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - _Omar E. Pol_, Sep 08 2011
%C A049453 First bisection of A036498. - _Bruno Berselli_, Nov 25 2012
%H A049453 G. C. Greubel, <a href="/A049453/b049453.txt">Table of n, a(n) for n = 0..1000</a>
%H A049453 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A049453 G.f.: x*(7+5*x)/(1-x)^3.
%F A049453 a(n) = 12*n + a(n-1) - 5 with n > 0, a(0)=0. - _Vincenzo Librandi_, Aug 06 2010
%F A049453 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _G. C. Greubel_, Jun 07 2017
%F A049453 From _Amiram Eldar_, Feb 18 2022: (Start)
%F A049453 Sum_{n>=1} 1/a(n) = 6 - sqrt(3)*Pi/2 - 2*log(2) - 3*log(3)/2.
%F A049453 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi + log(2) + sqrt(3)*log(2 + sqrt(3)) - 6. (End)
%F A049453 E.g.f.: exp(x)*x*(7 + 6*x). - _Elmo R. Oliveira_, Dec 12 2024
%p A049453 seq(binomial(6*n+1,2)/3, n=0..42); # _Zerinvary Lajos_, Jan 21 2007
%t A049453 s=0;lst={s};Do[s+=n++ +7;AppendTo[lst, s], {n, 0, 7!, 12}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 16 2008 *)
%t A049453 Table[n*(6*n + 1), {n,0,50}] (* _G. C. Greubel_, Jun 07 2017 *)
%o A049453 (PARI) x='x+O('x^50); concat([0], Vec(x*(7+5*x)/(1-x)^3)) \\ _G. C. Greubel_, Jun 07 2017
%Y A049453 Cf. A001318, A005449, A033568, A033570, A036498, A049452, A185019, A194454.
%Y A049453 Cf. A254963 (comment).
%K A049453 nonn,easy
%O A049453 0,2
%A A049453 Joe Keane (jgk(AT)jgk.org)