%I #17 Oct 26 2018 00:39:11
%S 1,3,3,3,4,5,6,8,10,13,17,22,29,38,50,66,87,115,152,200,264,349,461,
%T 609,804,1062,1402,1852,2446,3231,4267,5636,7444,9832,12987,17154,
%U 22657,29926,39528,52210,68961,91087,120312,158913,209899,277244
%N a(n) = floor( a(n-1)/a(1) + a(n-3)/a(3) + a(n-5)/a(5) + ... ), for n >= 3 with a(1) = 1 and a(2) = 3.
%H Iain Fox, <a href="/A022877/b022877.txt">Table of n, a(n) for n = 1..9000</a>
%F a(1)=1; a(2)=3; a(n) = floor(Sum_{i=1..floor(n/2)} a(n - (2*i-1))/a(2*i-1)). - _Iain Fox_, Oct 19 2018
%F a(n) ~ c * d^n, where d = 1.32084589099698002679195399789776925593378276999586161625509416650335137419... and c = 0.76500378031110004583172254717466388647997642917290688057501304595... - _Vaclav Kotesovec_, Oct 22 2018
%t a[1]:=1; a[2]:=3; a[n_]:=Floor[Sum[Mod[i,2] a[n-i]/a[i],{i,n-1}]]; Table[a[n], {n, 1, 15}] (* _Iain Fox_, Oct 19 2018 *)
%o (PARI) first(n) = my(res=vector(n)); for(x=1, n, res[x]=if(x<3, [1,3][x], floor(sum(i=1, x-1, (i%2)*res[x-i]/res[i])))); res \\ _Iain Fox_, Oct 19 2018
%Y Cf. A022859, A022865, A022871.
%Y Cf. A022860, A022866, A022872, A022878.
%K nonn
%O 1,2
%A _Clark Kimberling_