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

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, 764, 1102, 1591, 2296, 3313, 4782, 6901, 9960, 14375, 20747, 29944, 43217, 62373, 90021, 129925, 187516, 270636, 390601, 563742, 813631, 1174288, 1694813, 2446070

Offset: 0

Author

Roger L. Bagula, Nov 25 2010

Keywords

• nonn
• easy

Crossrefs

Cf. A107293.

Programs

Maple

A107293 := proc(n)
    option remember;
    if n <=4 then
        op(n+1,[0,0,0,0,1]) ;
    else
        procname(n-1)+procname(n-2)-procname(n-3)+procname(n-5) ;
    end if;
end proc:
A173693 := proc(n)
    ceil(A107293(n)/2) ;
end proc: # R. J. Mathar, Feb 18 2016

Mathematica

M = {{0, 1, 0, 0, 0},
{0, 0, 1, 0, 0},
{0, 0, 0, 1, 0},
{0, 0, 0, 0, 1},
{1, 0, -1, 1, 1}}
v[0] = {0, 0, 0, 0, 1}
v[n_] := v[n] = M.v[n - 1]
Table[v[n][[1]] - Floor[v[n][[1]]/2], {n, 0, 30}]

Formula

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

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