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 A131895 #34 Jun 02 2025 04:55:25
%S A131895 1,9,22,40,63,91,124,162,205,253,306,364,427,495,568,646,729,817,910,
%T A131895 1008,1111,1219,1332,1450,1573,1701,1834,1972,2115,2263,2416,2574,
%U A131895 2737,2905,3078,3256,3439,3627,3820,4018,4221,4429,4642,4860,5083,5311,5544
%N A131895 a(n) = (n + 2)*(5*n + 1)/2.
%C A131895 Row sums of triangle A131894.
%C A131895 Binomial transform of (1, 8, 5, 0, 0, 0, ...).
%H A131895 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A131895 a(n) = a(n-1) + 5*n + 3 (with a(0)=1). - _Vincenzo Librandi_, Nov 23 2010
%F A131895 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=1, a(1)=9, a(2)=22. - _Harvey P. Dale_, Sep 11 2015
%F A131895 From _Elmo R. Oliveira_, Oct 22 2024: (Start)
%F A131895 G.f.: (1 + 6*x - 2*x^2)/(1 - x)^3.
%F A131895 E.g.f.: (1 + 8*x + 5*x^2/2)*exp(x). (End)
%F A131895 Sum_{n>=0} 1/a(n) = (2 + sqrt(1+2/sqrt(5))*Pi + sqrt(5)*log(phi) + 5*log(5)/2)/9, where phi is the golden ratio (A001622). - _Amiram Eldar_, Jun 02 2025
%e A131895 a(2) = 22 = sum of row 2 terms of triangle A131894: (11 + 6 + 5).
%e A131895 a(2) = 22 = (1, 2, 1) dot (1, 8, 5) = (1 + 16 + 5).
%p A131895 A131895:=n->(n+2)*(5*n+1)/2; seq(A131895(n), n=0..50); # _Wesley Ivan Hurt_, Mar 26 2014
%t A131895 LinearRecurrence[{3,-3,1},{1,9,22},50] (* _Harvey P. Dale_, Sep 11 2015 *)
%o A131895 (PARI) a(n)=(n+2)*(5*n+1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A131895 Cf. A001622, A019952, A131894.
%K A131895 nonn,easy
%O A131895 0,2
%A A131895 _Gary W. Adamson_, Jul 24 2007
%E A131895 More terms from _Vladimir Joseph Stephan Orlovsky_, Dec 04 2008
%E A131895 Simpler definition from _Wesley Ivan Hurt_, Mar 26 2014