A173693 - OEIS

%I #14 Jul 01 2019 02:04:50

%S 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 764,1102,1591,2296,3313,4782,6901,9960,14375,20747,29944,43217,62373,

%U 90021,129925,187516,270636,390601,563742,813631,1174288,1694813,2446070

%N a(n) = ceiling(A107293(n)/2).

%F a(n) = A107293(n) - floor(A107293(n)/2) = ceiling(A107293(n)/2).

%F 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 A107293 := proc(n)

%p     option remember;

%p     if n <=4 then

%p         op(n+1,[0,0,0,0,1]) ;

%p     else

%p         procname(n-1)+procname(n-2)-procname(n-3)+procname(n-5) ;

%p     end if;

%p end proc:

%p A173693 := proc(n)

%p     ceil(A107293(n)/2) ;

%p end proc: # _R. J. Mathar_, Feb 18 2016

%t M = {{0, 1, 0, 0, 0},

%t {0, 0, 1, 0, 0},

%t {0, 0, 0, 1, 0},

%t {0, 0, 0, 0, 1},

%t {1, 0, -1, 1, 1}}

%t v[0] = {0, 0, 0, 0, 1}

%t v[n_] := v[n] = M.v[n - 1]

%t Table[v[n][[1]] - Floor[v[n][[1]]/2], {n, 0, 30}]

%Y Cf. A107293.

%K nonn,easy

%O 0,9

%A _Roger L. Bagula_, Nov 25 2010