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 A153127 #23 Oct 27 2024 18:58:54
%S A153127 6,33,80,147,234,341,468,615,782,969,1176,1403,1650,1917,2204,2511,
%T A153127 2838,3185,3552,3939,4346,4773,5220,5687,6174,6681,7208,7755,8322,
%U A153127 8909,9516,10143,10790,11457,12144,12851,13578,14325,15092,15879,16686,17513
%N A153127 a(n) = (2*n + 1)*(5*n + 6).
%H A153127 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A153127 a(n) = A153126(2*n+1) = A000566(2*(n+1)) - 1.
%F A153127 a(n) = a(n-1) + 20*n + 7 (with a(0)=6). - _Vincenzo Librandi_, Dec 27 2010
%F A153127 G.f.: (-6-15*x+x^2)/(-1+x)^3 - _Harvey P. Dale_, Jun 07 2021
%F A153127 Sum_{n>=0} 1/a(n) = 5/7 - sqrt(1+2/sqrt(5))*Pi/14 - sqrt(5)*log(phi)/14 - 5*log(5)/28 + 2*log(2)/7, where phi is the golden ratio (A001622). - _Amiram Eldar_, Aug 23 2022
%F A153127 From _Elmo R. Oliveira_, Oct 27 2024: (Start)
%F A153127 E.g.f.: exp(x)*(6 + 27*x + 10*x^2).
%F A153127 a(n) = A005408(n)*A016861(n+1).
%F A153127 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A153127 Table[(2n+1)(5n+6),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{6,33,80},50] (* _Harvey P. Dale_, Jun 07 2021 *)
%o A153127 (PARI) a(n)=(2*n+1)*(5*n+6) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A153127 Cf. A000566, A001622, A005408, A016861, A019952, A033571, A153126.
%K A153127 nonn,easy
%O A153127 0,1
%A A153127 _Reinhard Zumkeller_, Dec 20 2008