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 A103420 #22 Oct 23 2024 17:01:02
%S A103420 0,1,0,2,2,4,5,11,17,28,44,75,123,203,330,541,883,1444,2357,3848,6271,
%T A103420 10214,16624,27051,43995,71523,116223,188790,306554,497624,807553,
%U A103420 1310177,2125126,3446237,5587517,9057611,14680337,23789891,38546834,62449682,101163024
%N A103420 Number of compositions of n in which the least part is even.
%H A103420 Alois P. Heinz, <a href="/A103420/b103420.txt">Table of n, a(n) for n = 1..2000</a> (first 1000 terms from Robert Israel)
%F A103420 G.f.: Sum((1-x)^2*x^(2*n)/((1-x-x^(2*n))*(1-x-x^(2*n+1))), n=1..infinity).
%F A103420 G.f.: Sum(x^(2*n)/((1-x)^n*(1+x^n)),n=1..infinity). - _Vladeta Jovovic_, Mar 02 2008
%F A103420 a(n) ~ 1/sqrt(5) * ((1+sqrt(5))/2)^(n-1). - _Vaclav Kotesovec_, May 01 2014
%p A103420 N:= 50: # for a(1) .. a(N)
%p A103420 G:= add(x^(2*n)/((1-x)^n*(1+x^n)),n=1..N/2):
%p A103420 S:= series(G,x,N+1):
%p A103420 [seq(coeff(S,x,i),i=1..N)]; # _Robert Israel_, Oct 23 2024
%p A103420 # second Maple program:
%p A103420 b:= proc(n, m) option remember; `if`(n=0, 1-
%p A103420 irem(m, 2), add(b(n-j, min(m, j)), j=1..n))
%p A103420 end:
%p A103420 a:= n-> b(n, infinity):
%p A103420 seq(a(n), n=1..42); # _Alois P. Heinz_, Oct 23 2024
%t A103420 Rest[ CoefficientList[ Series[ Expand[ Sum[(1 - x)^2*x^(2n)/((1 - x - x^(2n))*(1 - x - x^(2n + 1))), {n, 40}]], {x, 0, 40}], x]] (* _Robert G. Wilson v_, Feb 05 2005 *)
%Y A103420 Cf. A103419, A103421, A103422, A027187, A027193, A026804, A026805.
%K A103420 easy,nonn
%O A103420 1,4
%A A103420 _Vladeta Jovovic_, Feb 04 2005
%E A103420 More terms from _Robert G. Wilson v_, Feb 05 2005