login
Expansion of 1/(1-x^2) + x/(1-x^3) + x^2/(1-x^4).
1

%I #23 Dec 14 2023 05:31:52

%S 1,1,2,0,2,0,2,1,1,0,3,0,1,1,2,0,2,0,2,1,1,0,3,0,1,1,2,0,2,0,2,1,1,0,

%T 3,0,1,1,2,0,2,0,2,1,1,0,3,0,1,1,2,0,2,0,2,1,1,0,3,0,1,1,2,0,2,0,2,1,

%U 1,0,3,0,1,1,2,0,2,0,2,1,1,0,3,0,1,1,2,0,2,0,2,1,1,0,3,0,1,1,2,0,2,0,2,1,1

%N Expansion of 1/(1-x^2) + x/(1-x^3) + x^2/(1-x^4).

%C Periodic {1,1,2,0,2,0,2,1,1,0,3,0}. Diagonal sums of A117198.

%C Number of divisors of n+2 in {2,3,4}. - _Wesley Ivan Hurt_, Jun 11 2023

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,0,1,1,1).

%F G.f.: (1+2x+4x^2+3x^3+3x^4)/(1+x+x^2-x^4-x^5-x^6).

%F a(n) = - a(n-1) - a(n-2) + a(n-4) + a(n-5) + a(n-6). - _Wesley Ivan Hurt_, Jun 11 2023

%t CoefficientList[ Series[1/(1 - x^2) + x/(1 - x^3) + x^2/(1 - x^4), {x, 0, 105}], x] (* _Robert G. Wilson v_, Mar 14 2006 *)

%t LinearRecurrence[{-1,-1,0,1,1,1},{1,1,2,0,2,0},120] (* or *) PadRight[ {},120,{1,1,2,0,2,0,2,1,1,0,3,0}] (* _Harvey P. Dale_, Dec 22 2013 *)

%K easy,nonn

%O 0,3

%A _Paul Barry_, Mar 02 2006

%E More terms from _Robert G. Wilson v_, Mar 14 2006