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 A055989 #34 Jul 02 2025 16:02:00
%S A055989 1,3,10,36,131,476,1728,6272,22765,82629,299915,1088589,3951206,
%T A055989 14341527,52054840,188941273,685792227,2489191330,9034913540,
%U A055989 32793647355,119029728628,432037221840,1568147413312,5691839002677,20659429692245,74986666876571,272175964826781
%N A055989 a(n) is its own 4th difference.
%C A055989 Number of compositions of 4*n-3 into parts 1 and 4. - _Seiichi Manyama_, Feb 03 2024
%H A055989 Vincenzo Librandi, <a href="/A055989/b055989.txt">Table of n, a(n) for n = 1..1000</a>
%H A055989 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,4,-1).
%F A055989 a(n) = 5*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) = a(n-1) + A055988(n) = A055990(n) - A055990(n-1) = A055991(n) - 2*A055991(n-1) + A055991(n-2).
%F A055989 G.f.: x*(1-x)^2/(1 - 5*x + 6*x^2 - 4*x^3 + x^4). - _Colin Barker_ Apr 04 2012
%t A055989 CoefficientList[Series[(1-x)^2/(1-5*x+6*x^2-4*x^3+x^4),{x,0,40}],x] (* _Vincenzo Librandi_, Apr 05 2012 *)
%t A055989 LinearRecurrence[{5,-6,4,-1},{1,3,10,36},30] (* _Harvey P. Dale_, Jan 10 2014 *)
%o A055989 (Magma) I:=[1, 3, 10, 36]; [n le 4 select I[n] else 5*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Apr 05 2012
%Y A055989 Cf. A055988, A055990, A055991 for the other differences of a(n). See A000079, A001906, A052529 for examples of sequences which are respectively their own first, second and third differences.
%Y A055989 Cf. A003269.
%K A055989 nonn,easy
%O A055989 1,2
%A A055989 _Henry Bottomley_, Jun 02 2000
%E A055989 More terms from _James Sellers_, Jun 05 2000