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 A084172 #24 Apr 15 2024 11:11:12
%S A084172 1,2,4,9,19,40,82,167,337,678,1360,2725,5455,10916,21838,43683,87373,
%T A084172 174754,349516,699041,1398091,2796192,5592394,11184799,22369609,
%U A084172 44739230,89478472,178956957,357913927,715827868,1431655750,2863311515
%N A084172 a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4).
%C A084172 Original name was: Generalized Jacobsthal numbers.
%C A084172 Sums of rows of the triangle in A109225. - _Reinhard Zumkeller_, Jun 23 2005
%H A084172 Vincenzo Librandi, <a href="/A084172/b084172.txt">Table of n, a(n) for n = 0..1000</a>
%H A084172 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,2).
%F A084172 a(n) = 2^(n+2)/3 - (-1)^n/12 - (2*n+1)/4.
%F A084172 G.f: (2*x^3 - x^2 - x + 1)/( (x+1)*(1-2*x)*(1-x)^2).
%F A084172 a(n+2) = a(n+1) + 2*a(n) + n, a(0)=0, a(1)=2.
%F A084172 a(n) = A001045(n+1) + A083579(n).
%F A084172 a(n+1) = 2*a(n) + floor(n/2). _Franklin T. Adams-Watters_, Oct 17 2013
%F A084172 a(n)+a(n+1) = A095768(n+1). - _R. J. Mathar_, Apr 15 2024
%t A084172 LinearRecurrence[{3,-1,-3,2},{1,2,4,9},40] (* _Harvey P. Dale_, Nov 13 2013 *)
%o A084172 (Magma) [2^(n+2)/3-(-1)^n/12-(2*n+1)/4: n in [0..35]]; // _Vincenzo Librandi_, Jul 05 2011
%K A084172 easy,nonn
%O A084172 0,2
%A A084172 _Paul Barry_, May 18 2003