login
Denominators of correlation kernels arising in adding a list of numbers in base 3 considering the distribution of number of carries.
2

%I #15 Dec 21 2015 12:53:41

%S 3,3,9,9,27,1,81,81,243,243,729,1,2187,2187,6561,6561,19683,1,59049,

%T 59049,177147,177147,531441,1,1594323,1594323,4782969,4782969,

%U 14348907,1,43046721,43046721,129140163,129140163,387420489,1,1162261467

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

%C From example 4, p. 645 of Borodin.

%H Alexei Borodin, Persi Diaconis, and Jason Fulman, <a href="http://dx.doi.org/10.1090/S0273-0979-2010-01306-9 ">On adding a list of numbers (and other one-dependent determinantal processes)</a>, Bull. AMS, Volume 47, Number 4, October 2010, Pages 639-670.

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, -27).

%F 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.

%p A214439 := proc(n)

%p (1+t+2*t^2/3+t^3/3+t^4/9)/3/(1+t^6/27) ;

%p coeftayl(%,t=0,n+1) ;

%p denom(%) ;

%p end proc:

%p seq(A214439(n),n=-1..80) ; # _R. J. Mathar_, Jul 21 2012

%t 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 *)

%Y Cf. A214438 (numerators).

%K nonn,frac

%O -1,1

%A _Jonathan Vos Post_, Jul 17 2012