[seqfan] useful complifification in A130102?

[Rainer Rosenthal]

in http://www.research.att.com/~njas/sequences/A130102
we learn:

a(n)=2^n-2n+2*C(2, n)-4*C(1, n)+2*C(0, n); 

The essence of that is:

      a(2) = 2,   a(n) = 2^n - 2n  for n /= 2

since we can write  a(n) = 2^n - 2n + Z(n) where Z(n) is given by the
following little table:

:
:  n       C(0,n)  C(1,n)  C(2,n)                Z(n)
: ------------------------------------------------------------------
:  0         1       1       1        2*1 - 4*1 + 2*1 = 0
:  1         0       1       2        2*0 - 4*1 + 2*2 = 0
:  2         0       0       1        2*0 - 4*0 + 2*1 = 2
:  3 etc.    0       0       0        2*0 - 4*0 + 2*0 = 0
:____________________________________________________________________
:
: Table 1: function Z(n) demasked
:

Is there any value in having such a complicated expression here?

Cheers,
Rainer