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 A081662 #24 Feb 14 2023 08:53:30
%S A081662 1,3,7,13,22,35,54,82,124,188,287,442,687,1077,1701,2703,4316,6917,
%T A081662 11116,17900,28866,46598,75277,121668,196717,318135,514579,832417,
%U A081662 1346674,2178743,3525042,5703382,9227992,14930912,24158411,39088798
%N A081662 Partial sums of n + Fibonacci(n+1).
%H A081662 Harvey P. Dale, <a href="/A081662/b081662.txt">Table of n, a(n) for n = 0..1000</a>
%H A081662 W. Kuszmaul, <a href="http://arxiv.org/abs/1509.08216">Fast Algorithms for Finding Pattern Avoiders and Counting Pattern Occurrences in Permutations</a>, arXiv preprint arXiv:1509.08216 [cs.DM], 2015-2017.
%H A081662 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,1,2,-1).
%F A081662 a(n) = (1 - 2*sqrt(5)/5)*(sqrt(5)/2 - 1/2)^n*(-1)^n + (sqrt(5)/2 + 1/2)^n*(2*sqrt(5)/5 + 1) + (n^2 + n - 2)/2.
%F A081662 G.f.: (x^3 + x - 1)/((1-x)^3*(x^2 + x - 1)).
%F A081662 a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5); a(0)=1, a(1)=3, a(2)=7, a(3)=13, a(4)=22. - _Harvey P. Dale_, Nov 19 2011
%F A081662 E.g.f.: exp(x)*(x^2 + 2*x - 2)/2 + 2*exp(x/2)*(5*cosh(sqrt(5)*x/2) + 2*sqrt(5)*sinh(sqrt(5)*x/2))/5. - _Stefano Spezia_, Feb 13 2023
%t A081662 Accumulate[Table[Total[{n,Fibonacci[n+1]}],{n,0,40}]] (* or *) LinearRecurrence[ {4,-5,1,2,-1},{1,3,7,13,22},41] (* _Harvey P. Dale_, Nov 19 2011 *)
%Y A081662 Cf. A081659, A000045.
%K A081662 easy,nonn
%O A081662 0,2
%A A081662 _Paul Barry_, Mar 26 2003