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A173693 a(n) = ceiling(A107293(n)/2).

%I A173693 #14 Jul 01 2019 02:04:50
%S A173693 0,0,0,0,1,1,1,1,2,2,3,5,7,10,14,20,28,41,59,85,122,176,254,367,529,
%T A173693 764,1102,1591,2296,3313,4782,6901,9960,14375,20747,29944,43217,62373,
%U A173693 90021,129925,187516,270636,390601,563742,813631,1174288,1694813,2446070
%N A173693 a(n) = ceiling(A107293(n)/2).
%F A173693 a(n) = A107293(n) - floor(A107293(n)/2) = ceiling(A107293(n)/2).
%F A173693 Conjecture: a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-5) + a(n-31) - a(n-32) - a(n-33) + a(n-34) - a(n-36). - _R. J. Mathar_, Feb 18 2016
%p A173693 A107293 := proc(n)
%p A173693     option remember;
%p A173693     if n <=4 then
%p A173693         op(n+1,[0,0,0,0,1]) ;
%p A173693     else
%p A173693         procname(n-1)+procname(n-2)-procname(n-3)+procname(n-5) ;
%p A173693     end if;
%p A173693 end proc:
%p A173693 A173693 := proc(n)
%p A173693     ceil(A107293(n)/2) ;
%p A173693 end proc: # _R. J. Mathar_, Feb 18 2016
%t A173693 M = {{0, 1, 0, 0, 0},
%t A173693 {0, 0, 1, 0, 0},
%t A173693 {0, 0, 0, 1, 0},
%t A173693 {0, 0, 0, 0, 1},
%t A173693 {1, 0, -1, 1, 1}}
%t A173693 v[0] = {0, 0, 0, 0, 1}
%t A173693 v[n_] := v[n] = M.v[n - 1]
%t A173693 Table[v[n][[1]] - Floor[v[n][[1]]/2], {n, 0, 30}]
%Y A173693 Cf. A107293.
%K A173693 nonn,easy
%O A173693 0,9
%A A173693 _Roger L. Bagula_, Nov 25 2010