[seqfan] Re: simple sequence not in OEIS

[Ed Jeffery]

Dave,

Second differences of your terms seem to be given identically by A196537 (
http://oeis.org/A196537) with the same recurrence.

LEJ

>Number of permutations of 1..n for which the partial sum of signed displacements does not exceed 2.

>e.g. n=5

>s(i)             3  1  4  2  5
>s(i)-i           2 -1  1 -2  0
>partial sum      2  1  2  0  0   // max = 2 so counted

>s(i)             3  1  4  5  2
>s(i)-i           2 -1  1  1 -3
>partial sum      2  1  2  3  0   // max = 3 so not counted

>a(n) = 1, 1, 2, 6, 12, 25, 57, 124, 268, 588, 1285, 2801, 6118, 13362, ...

>seems to be
>g.f. 1/(1-n-n^2-3*n^3-n^4)


>dave