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 A081663 #17 May 06 2024 14:31:40
%S A081663 1,3,9,25,66,169,425,1058,2621,6485,16066,39921,99601,249666,628917,
%T A081663 1592029,4048866,10341577,26517113,68226722,176065901,455514533,
%U A081663 1181040514,3067684065,7980068641,20784441474,54188706405,141395801773
%N A081663 a(n) = Fibonacci(2n+1) + n*2^(n-1).
%C A081663 Binomial transform of n + Fibonacci(n+1), A081659.
%H A081663 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-17,16,-4).
%F A081663 a(n) = A001519(n)+A001787(n).
%F A081663 a(n) = 7*a(n-1)-17*a(n-2)+16*a(n-3)-4*a(n-4). G.f.: -(3*x^3-5*x^2+4*x-1) / ((2*x-1)^2*(x^2-3*x+1)). - _Colin Barker_, Jun 04 2013
%t A081663 Table[Fibonacci[2n+1]+n 2^(n-1),{n,0,30}] (* or *) LinearRecurrence[{7,-17,16,-4},{1,3,9,25},30] (* _Harvey P. Dale_, Sep 17 2020 *)
%Y A081663 Cf. A000045, A001519, A001787, A081659.
%K A081663 easy,nonn
%O A081663 0,2
%A A081663 _Paul Barry_, Mar 26 2003
%E A081663 Definition corrected by Matt Lehman, May 21 2010