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 A124861 #21 May 19 2025 09:43:40
%S A124861 1,1,4,11,29,80,219,597,1632,4459,12181,33280,90923,248405,678656,
%T A124861 1854123,5065557,13839360,37809835,103298389,282216448,771029675,
%U A124861 2106492245,5755043840,15723072171,42956232021,117358608384,320629680811,875976578389,2393212518400,6538378193579
%N A124861 Expansion of 1/(1-x-3*x^2-4*x^3-2*x^4).
%C A124861 Diagonal sums of number triangle A124860.
%H A124861 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,4,2).
%F A124861 a(n) = a(n-1)+3*a(n-2)+4*a(n-3)+2*a(n-4); a(n) = Sum_{k=0..floor(n/2)} J(n-k+1)*C(n-k,k) where J(n) = A001045(n). - corrected by _Harvey P. Dale_, Apr 22 2011
%F A124861 G.f.: 1 + x/(G(0) - x) where G(k) = 1 - 8*x - 2*k*x + k + 2*x*(k+1)*(k+5)/G(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Apr 09 2013
%t A124861 LinearRecurrence[{1,3,4,2},{1,1,4,11},30] (* or *) CoefficientList[ Series[ 1/(1-x-3x^2-4x^3-2x^4),{x,0,30}],x] (* _Harvey P. Dale_, Apr 22 2011 *)
%o A124861 (PARI) Vec(1/(1-x-3*x^2-4*x^3-2*x^4) + O(x^40)) \\ _Michel Marcus_, May 19 2025
%K A124861 easy,nonn
%O A124861 0,3
%A A124861 _Paul Barry_, Nov 10 2006
%E A124861 More terms from _Michel Marcus_, May 19 2025