[seqfan] A005377 discrepancy

[Sean A. Irvine]

Although A005377 is about discrepant sequences, I'm actually getting a
discrepancy computing the terms of this sequence when using Niederreiter's
approach as compared to the values and generating function in the OEIS
entry.

Niederreiter gives (p. 59) the following formulas for a(n):

Let N(b,n) = (1/n) * Sum_{d|n} mobius(n/d) * b^d.

Let M(b,n) = Sum_{k=1..n} N(b,k) with M(b,0) = 0.

Let r = r(b,n) be the largest value r such that M(b,r) <= n.

Finally, a(n) = Sum_{h=1..r} (h-1) * N(4, h) + r * (n - M(4, r)).

The OEIS entry contains the g.f. (x^4+x^10)/(1-2*x+x^2), which looking at
the history is probably based on Plouffe's 1992 conjectured g.f.

Both approaches get the same values for a(0)-a(29) (which also coincide
with Table IV in Niederreiter -- except that the offset is off by 1).
However, for a(30) and later terms the two approaches give different
values; Niederreiter's approach gives a(30)=49 while the g.f. a(30)=48.

I would appreciate someone else trying Niederreiter's formula just to make
sure I didn't make some mistake with that.

I am inclined to replace the values from a(30) onwards with what I think
are the correct values based on Niederreiter's formula and mark the
existing generating function as incorrect.  I also think the offset should
be corrected to be consistent with Niederreiter's table and other related
sequences like A005356.

Sean.