[seqfan] Re: A000134

[Gerald McGarvey]

This inspired me to look at the shape of the Bessel function of order 0,
in PARI:    b(n) = besselj(0,n-1/2)*besselj(0,n+1/2)

The function b(n) appears to asymptotically approach the following function:

f(n) = 1/(n*Pi) * (sin(2*n) + cos(1))

The difference between these functions also looks like a damped sinusoid,
around   1/(4*n^2*Pi)*cos(2*n)

Regards,
Gerald McGarvey

At 10:03 PM 8/26/2009, David Wilson wrote:
>For most n, A000134(n) = round(pi*(n-1/4)). For 1 <= n <= 1000, the only
>exception is n = 2.
>
>
>
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