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 A157728 #30 Dec 12 2024 10:55:33 %S A157728 1,4,9,17,30,51,85,140,229,373,606,983,1593,2580,4177,6761,10942, %T A157728 17707,28653,46364,75021,121389,196414,317807,514225,832036,1346265, %U A157728 2178305,3524574,5702883,9227461,14930348,24157813,39088165,63245982,102334151 %N A157728 a(n) = Fibonacci(n) - 4. %C A157728 Partial sums of A071679. - _R. J. Mathar_, Oct 12 2010 %H A157728 Vincenzo Librandi, <a href="/A157728/b157728.txt">Table of n, a(n) for n = 5..287</a> %H A157728 Paul Barry, <a href="https://arxiv.org/abs/2412.05461">The Triple Riordan Group</a>, arXiv:2412.05461 [math.CO], 2024. See pp. 5, 10. %H A157728 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1). %F A157728 From _R. J. Mathar_, Oct 12 2010: (Start) %F A157728 a(n) = 2*a(n-1) - a(n-3). %F A157728 G.f.: x^5*(1+x)^2/((x-1)*(x^2+x-1)). (End) %t A157728 Fibonacci[Range[5,40]]-4 (* or *) LinearRecurrence[{2,0,-1},{1,4,9},40] (* _Harvey P. Dale_, Jan 17 2022 *) %o A157728 (Magma) [ Fibonacci(n) - 4: n in [5..50] ]; // _Vincenzo Librandi_, Apr 24 2011 %o A157728 (Haskell) %o A157728 a157728 = subtract 4 . a000045 -- _Reinhard Zumkeller_, Oct 31 2013 %o A157728 (PARI) a(n)=fibonacci(n) - 4 \\ _Charles R Greathouse IV_, Jun 11 2015 %Y A157728 Cf. A000045, A001611, A000071, A157725, A001911, A157726, A006327, A157727, A157728, A157729, A167616. %K A157728 nonn,easy %O A157728 5,2 %A A157728 _N. J. A. Sloane_, Jun 26 2010