A165438 - OEIS

A165438

Number a(n) of alternative sets of orthogonal contrasts available to partition variation between n levels of a categorical factor in analysis of variance, with each set described by a unique general linear model.

1, 3, 4, 8, 15, 34, 69, 152, 332, 751, 1698, 3905, 9020, 21051, 49356, 116505, 276217, 658091, 1573835, 3778152, 9098915, 21980209, 53241777, 129294912, 314714273, 767700735, 1876437054, 4595005570, 11271747564, 27695048780

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OFFSET

3,2

COMMENTS

Each set has n-1 orthogonal contrasts.

REFERENCES

Doncaster, C. P. & Davey, A. J. H. (2007) Analysis of Variance and Covariance: How to Choose and Construct Models for the Life Sciences. Cambridge: Cambridge University Press.

LINKS

Table of n, a(n) for n=3..32.

C. P. Doncaster, Contrast sets

C. P. Doncaster, Orthogonal contrasts

C. P. Doncaster & A. J. H. Davey, Analysis of Variance and Covariance

FORMULA

For n=5,6,7: a(n) = -mod(n,2)*a([n-mod{n,2}]/2) + sum_{k=3..n-1} a[k]

For n>7: a(n) = -mod(n,2)*a([n-mod{n,2}]/2) + 2*a(n-1) + b(n) - b(n-1)

where b(m) = 0^mod(log(m,2),1) + mod(m-1,2)*0.5*a([m-mod{m,2}]/2)*(a[{m-mod(m,2)}/2]-1)

+ sum_{k=3..(m-1-mod[m-1,2])/2} a(m-k)*(a[k]-1)

EXAMPLE

A factor 'A' with n = 5 levels, has a(5) = 4 alternative sets of orthogonal