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 A027949 #24 Sep 08 2022 08:44:49
%S A027949 1,4,25,97,309,894,2462,6610,17519,46135,121115,317484,831660,2177872,
%T A027949 5702389,14929789,39087537,102333450,267913514,701407870,1836310955,
%U A027949 4807525939,12586267895,32951278872,86267569944,225851432284,591286728337,1548008754265
%N A027949 a(n) = T(2n,n+1), T given by A027948.
%H A027949 Colin Barker, <a href="/A027949/b027949.txt">Table of n, a(n) for n = 1..1000</a>
%H A027949 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,13,-6,1).
%F A027949 For n>1, a(n) = Fibonacci(2*n+4) - (2*n^2 + 3*n + 3).
%F A027949 a(1)=1, a(2)=4, a(3)=25, a(4)=97, a(5)=309, a(6)=894, a(n) = 6*a(n-1) - 13*a(n-2) +13*a(n-3) -6*a(n-4) +a(n-5). - _Harvey P. Dale_, Apr 20 2012
%F A027949 G.f.: x*(1 -2*x +14*x^2 -14*x^3 +6*x^4 -x^5)/((1-x)^3*(1-3*x+x^2)). - _Colin Barker_, Nov 19 2014
%F A027949 a(n) = Sum_{j=0..n-1} binomial(2*n-j, j+3), with a(1)=1. - _G. C. Greubel_, Sep 29 2019
%p A027949 with(combinat); seq(`if`(n=1, 1, fibonacci(2*n+4) -(2*n^2 +3*n +3)), n=1..40); # _G. C. Greubel_, Sep 29 2019
%t A027949 Join[{1},Table[Fibonacci[2n+4]-2n^2-3n-3,{n,2,40}]] (* or *) Join[ {1}, LinearRecurrence[{6,-13,13,-6,1}, {4,25,97,309,894}, 40]] (* _Harvey P. Dale_, Apr 20 2012 *)
%t A027949 CoefficientList[Series[(x^5-6x^4+14x^3-14x^2+2x-1)/((x-1)^3(x^2-3x+1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Nov 20 2014 *)
%o A027949 (PARI) Vec(x*(x^5-6*x^4+14*x^3-14*x^2+2*x-1)/((x-1)^3*(x^2-3*x+1)) + O(x^40)) \\ _Colin Barker_, Nov 19 2014
%o A027949 (PARI) vector(40, n, if(n==1,1,fibonacci(2*n+4) -(2*n^2 +3*n +3)) ) \\ _G. C. Greubel_, Sep 29 2019
%o A027949 (Magma) [1] cat [Fibonacci(2*n+4) -(2*n^2 +3*n +3): n in [2..40]]; // _G. C. Greubel_, Sep 29 2019
%o A027949 (Sage) [1]+[fibonacci(2*n+4) -(2*n^2 +3*n +3) for n in (2..40)] # _G. C. Greubel_, Sep 29 2019
%o A027949 (GAP) Concatenation([1], List([2..40], n-> Fibonacci(2*n+4) -(2*n^2 +3*n +3)) ); # _G. C. Greubel_, Sep 29 2019
%Y A027949 Cf. A000045, A027948.
%K A027949 nonn,easy
%O A027949 1,2
%A A027949 _Clark Kimberling_
%E A027949 More terms from _Harvey P. Dale_, Apr 20 2012