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A063942 Follow k with k-1 and k-2.

%I A063942 #31 Dec 28 2024 11:50:44
%S A063942 1,0,-1,2,1,0,3,2,1,4,3,2,5,4,3,6,5,4,7,6,5,8,7,6,9,8,7,10,9,8,11,10,
%T A063942 9,12,11,10,13,12,11,14,13,12,15,14,13,16,15,14,17,16,15,18,17,16,19,
%U A063942 18,17,20,19,18,21,20,19,22,21,20,23,22,21,24,23,22,25,24,23,26,25,24,27,26,25,28,27,26,29,28,27,30,29,28,31,30,29,32
%N A063942 Follow k with k-1 and k-2.
%H A063942 Harry J. Smith, <a href="/A063942/b063942.txt">Table of n, a(n) for n = 0..1000</a>
%H A063942 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A063942 G.f.: ( 1-x^2+2*x^3-x ) / ( (1+x+x^2)*(x-1)^2 ). - _R. J. Mathar_, Jul 14 2015
%F A063942 a(3n) = n+1. a(3n+1) = n. a(3n+2) = n-1. - _R. J. Mathar_, Jan 10 2017
%F A063942 a(n) = (3*n-3-12*cos(2*(n-5)*Pi/3)+4*sqrt(3)*sin(2*(n-5)*Pi/3))/9. - _Wesley Ivan Hurt_, Sep 29 2017
%F A063942 E.g.f.: exp(x)*(x - 1)/3 + 4*exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2))/9. - _Stefano Spezia_, Oct 02 2022
%F A063942 Sum_{n>=6} (-1)^n/a(n) = 3*(log(2)-1/2). - _Amiram Eldar_, Oct 04 2022
%t A063942 LinearRecurrence[{1, 0, 1, -1}, {1, 0, -1, 2}, 100] (* _Amiram Eldar_, Oct 04 2022 *)
%o A063942 (PARI) a(n) = (n\3)-(n%3)+1
%Y A063942 Cf. A028242.
%K A063942 easy,sign
%O A063942 0,4
%A A063942 _Jason Earls_, Sep 01 2001