The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 contrasts, each with n - 1 = 4 contrasts. The corresponding alternative general linear models describing contrasts 'B', 'C', 'D', 'E' are: B + C(B) + D(B) + E(D B) B + C(B) + D(C B) + E(D C B) B + C(B) + D(C B) + E(C B) B + C(B) + D(B) + E(B) CROSSREFS Sequence in context: A337438 A007486 A027977 * A293781 A202025 A227615 Adjacent sequences: A165435 A165436 A165437 * A165439 A165440 A165441 KEYWORD nonn AUTHOR C. Patrick Doncaster (cpd(AT)soton.ac.uk), Sep 18 2009 EXTENSIONS Corrected and edited by C. P. Doncaster (cpd(AT)soton.ac.uk), Mar 02 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 27 09:16 EST 2022. Contains 358367 sequences. (Running on oeis4.)