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 A192136 #25 Nov 16 2024 21:35:12
%S A192136 1,2,8,19,35,56,82,113,149,190,236,287,343,404,470,541,617,698,784,
%T A192136 875,971,1072,1178,1289,1405,1526,1652,1783,1919,2060,2206,2357,2513,
%U A192136 2674,2840,3011,3187,3368,3554,3745,3941,4142,4348,4559,4775,4996,5222,5453,5689
%N A192136 a(n) = (5*n^2 - 3*n + 2)/2.
%C A192136 Binomial transform of [1, 1, 5, 0, 0, 0, 0, 0, ...]. - _Johannes W. Meijer_, Jul 07 2011
%H A192136 Vincenzo Librandi, <a href="/A192136/b192136.txt">Table of n, a(n) for n = 0..10000</a>
%H A192136 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A192136 a(n) = (5*n^2 - 3*n + 2)/2.
%F A192136 a(n) = 2*a(n-1) - a(n-2) + 5.
%F A192136 a(n) = a(n-1) + 5*n - 4.
%F A192136 a(n) = 5*binomial(n+2,2) - 9*n - 4.
%F A192136 a(n) = A000217(n+1) - A000217(n) + 5*A000217(n-1); triangular numbers. - _Johannes W. Meijer_, Jul 07 2011
%F A192136 O.g.f.: (1-x+5*x^2)/(1-x)^3.
%F A192136 From _Elmo R. Oliveira_, Nov 16 2024: (Start)
%F A192136 E.g.f.: exp(x)*(2 + 2*x + 5*x^2)/2.
%F A192136 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A192136 Table[(5n^2-3n+2)/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{1,2,8},50] (* _Harvey P. Dale_, Aug 08 2016 *)
%o A192136 (Magma) A192136:=func< n | (5*n^2-3*n+2)/2 >; [ A192136(n): n in [0..50] ]; // _Klaus Brockhaus_, Jun 27 2011
%o A192136 (PARI) a(n)=n*(5*n-3)/2+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A192136 Cf. A000124, A000217, A002522, A006137, A130883, A140063, A140064, A143689.
%K A192136 nonn,easy
%O A192136 0,2
%A A192136 _Eric Werley_, Jun 24 2011