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 A075111 #10 Jul 05 2025 05:18:30
%S A075111 0,1,1,1,3,6,10,18,34,63,115,211,389,716,1316,2420,4452,8189,15061,
%T A075111 27701,50951,93714,172366,317030,583110,1072507,1972647,3628263,
%U A075111 6673417,12274328,22576008,41523752,76374088,140473849,258371689
%N A075111 a(n) = Sum_{i=0..floor(n/2)} (-1)^(i+floor(n/2))*T(2i+e), where T(n) are tribonacci numbers (A000073) and e = (1/2)(1-(-1)^n).
%C A075111 a(n) is the convolution of T(n) with the sequence (1,0,-1,0,1,0,-1,0,....) A056594.
%C A075111 The number of ways to place non-overlapping Young diagrams of shape (3,1) on an 3 by n rectangle. - _Per Alexandersson_, Jul 01 2025
%H A075111 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,1,1).
%F A075111 a(n) = a(n-1)+2a(n-3)+a(n-4)+a(n-5), a(0)=0, a(1)=1, a(2)=1, a(3)=1, a(4)=3.
%F A075111 G.f.: x/(1 - x - 2*x^3 - x^4 - x^5).
%t A075111 CoefficientList[Series[x/(1 - x - 2*x^3 - x^4 - x^5), {x, 0, 40}], x]
%Y A075111 Cf. A000073, A056594, A074662, A074677, A074678.
%K A075111 easy,nonn
%O A075111 0,5
%A A075111 Mario Catalani (mario.catalani(AT)unito.it), Sep 01 2002