A214439 Denominators of correlation kernels arising in adding a list of numbers in base 3 considering the distribution of number of carries.

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

Table of n, a(n) for n=-1..35.

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

Adjacent sequences: A214436 A214437 A214438 * A214440 A214441 A214442

Keyword

nonn,frac

Author

Jonathan Vos Post, Jul 17 2012

Status

approved