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 A228078 #24 Nov 14 2024 15:07:05
%S A228078 0,0,2,5,12,26,55,114,234,477,968,1958,3951,7958,16006,32157,64548,
%T A228078 129474,259559,520106,1041810,2086205,4176592,8359950,16730847,
%U A228078 33479406,66987470,134021309,268117644,536356682,1072909783,2146137378,4292788986,8586410013
%N A228078 a(n) = 2^n - Fibonacci(n) - 1.
%C A228078 a(n+1) = sum of n-th row of the triangle in A228074.
%H A228078 Reinhard Zumkeller, <a href="/A228078/b228078.txt">Table of n, a(n) for n = 0..1000</a>
%H A228078 Tamás Szakács, <a href="https://hdl.handle.net/2437/381856">Linear recursive sequences and factorials</a>, Ph. D. Thesis, Univ. Debrecen (Hungary, 2024). See p. 30.
%H A228078 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-1,2).
%F A228078 a(n) = A000079(n) - A000045(n) - 1 = A000225(n) - A000045(n) = A000079(n) - A001611(n) = A099036(n) - 1.
%F A228078 From _Colin Barker_, Mar 20 2015: (Start)
%F A228078 a(n) = 4*a(n-1)-4*a(n-2)-a(n-3)+2*a(n-4) for n>3.
%F A228078 G.f.: x^2*(3*x-2) / ((x-1)*(2*x-1)*(x^2+x-1)). (End)
%F A228078 a(n) = (-1+2^n+(((1-sqrt(5))/2)^n-((1+sqrt(5))/2)^n)/sqrt(5)). - _Colin Barker_, Nov 02 2016
%t A228078 Table[(2^n - Fibonacci[n] - 1), {n, 0, 40}] (* _Vincenzo Librandi_, Aug 16 2013 *)
%o A228078 (Haskell)
%o A228078 a228078 = subtract 1 . a099036
%o A228078 (Magma)
%o A228078 [2^n - Fibonacci(n) - 1: n in [0..40]]; // _Vincenzo Librandi_, Aug 16 2013
%o A228078 (PARI) concat([0,0], Vec(x^2*(3*x-2)/((x-1)*(2*x-1)*(x^2+x-1)) + O(x^100))) \\ _Colin Barker_, Mar 20 2015
%K A228078 nonn,easy
%O A228078 0,3
%A A228078 _Reinhard Zumkeller_, Aug 15 2013