A214438 - OEIS

%I #21 Dec 21 2015 12:54:02

%S 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,

%T 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,

%U -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

%N Numerator 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.

%C Periodic with period 12. - _Ray Chandler_, Sep 03 2015

%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_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 0, -1).

%F 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.

%p A214438 := 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         numer(%) ;

%p end proc:

%p seq(A214438(n),n=-1..80) ; # _R. J. Mathar_, Jul 21 2012

%t LinearRecurrence[{0, 1, 0, -1},{1, 1, 2, 1},82] (* _Ray Chandler_, Sep 03 2015 *)

%Y Cf. A214439 (denominators).

%K sign,frac

%O -1,3

%A _Jonathan Vos Post_, Jul 17 2012