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A214439
Denominators of correlation kernels arising in adding a list of numbers in base 3 considering the distribution of number of carries.
2
3, 3, 9, 9, 27, 1, 81, 81, 243, 243, 729, 1, 2187, 2187, 6561, 6561, 19683, 1, 59049, 59049, 177147, 177147, 531441, 1, 1594323, 1594323, 4782969, 4782969, 14348907, 1, 43046721, 43046721, 129140163, 129140163, 387420489, 1, 1162261467
OFFSET
-1,1
COMMENTS
From example 4, p. 645 of Borodin.
LINKS
Alexei Borodin, Persi Diaconis, and Jason Fulman, On adding a list of numbers (and other one-dependent determinantal processes), Bull. AMS, Volume 47, Number 4, October 2010, Pages 639-670.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, -27).
FORMULA
Denominators of: k(n) = 0 for n < -1; k(-1) = 1/3; k(n) = 0 for n = 4 + 6j, j >= 0; for others n >= 2, k(n) = (-1)^floor((n+1)/6) * (1/3)^ floor ((n+3)/4)* 2^delta(n) where delta(n) = 1 if n = 1 mod 6 and 0 else.
MAPLE
A214439 := proc(n)
(1+t+2*t^2/3+t^3/3+t^4/9)/3/(1+t^6/27) ;
coeftayl(%, t=0, n+1) ;
denom(%) ;
end proc:
seq(A214439(n), n=-1..80) ; # R. J. Mathar, Jul 21 2012
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, -27}, {3, 3, 9, 9, 27, 1, 81, 81, 243, 243, 729, 1}, 37] (* Ray Chandler, Sep 03 2015 *)
CROSSREFS
Cf. A214438 (numerators).
Sequence in context: A147510 A146474 A145957 * A287479 A128019 A056449
KEYWORD
nonn,frac
AUTHOR
Jonathan Vos Post, Jul 17 2012
STATUS
approved