A214438 Numerator of correlation kernels arising in adding a list of numbers in base 3 considering the distribution of number of carries.

1, 1, 2, 1, 1, 0, -1, -1, -2, -1, -1, 0, 1, 1, 2, 1, 1, 0, -1, -1, -2, -1, -1, 0, 1, 1, 2, 1, 1, 0, -1, -1, -2, -1, -1, 0, 1, 1, 2, 1, 1, 0, -1, -1, -2, -1, -1, 0, 1, 1, 2, 1, 1, 0, -1, -1, -2, -1, -1, 0, 1, 1, 2, 1, 1, 0, -1, -1, -2, -1, -1, 0, 1, 1, 2, 1, 1, 0, -1, -1, -2, -1

Offset

-1,3

Comments

From example 4, p. 645 of Borodin.

Periodic with period 12. - Ray Chandler, Sep 03 2015

Links

Table of n, a(n) for n=-1..80.

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, 1, 0, -1).

Formula

numerators 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

A214438 := proc(n)
        (1+t+2*t^2/3+t^3/3+t^4/9)/3/(1+t^6/27) ;
        coeftayl(%, t=0, n+1) ;
        numer(%) ;
end proc:
seq(A214438(n), n=-1..80) ; # R. J. Mathar, Jul 21 2012

Mathematica

LinearRecurrence[{0, 1, 0, -1}, {1, 1, 2, 1}, 82] (* Ray Chandler, Sep 03 2015 *)

Crossrefs

Cf. A214439 (denominators).

Sequence in context: A278347 A120936 A335294 * A173432 A101675 A348916

Adjacent sequences: A214435 A214436 A214437 * A214439 A214440 A214441

Keyword

sign,frac

Author

Jonathan Vos Post, Jul 17 2012

Status

approved