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

%I #6 Aug 04 2021 15:29:51

%S 1,-2,1,-3,3,-4,6,-7,10,-13,17,-23,30,-40,53,-70,93,-123,163,-216,286,

%T -379,502,-665,881,-1167,1546,-2048,2713,-3594,4761,-6307,8355,-11068,

%U 14662,-19423,25730,-34085,45153,-59815,79238

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

%C Diagonal sums of number triangle A117362.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,-1).

%F a(n)=a(n-2)-a(n-3); a(n)=sum{k=0..floor(n/2), (-1)^n*(C(k,n-2k)+2*C(k,n-2k-1))}.

%t CoefficientList[Series[(1-2x)/(1-x^2+x^3),{x,0,60}],x] (* or *) LinearRecurrence[ {0,1,-1},{1,-2,1},60] (* _Harvey P. Dale_, Aug 04 2021 *)

%Y Cf. A109248, A007307.

%K easy,sign

%O 0,2

%A _Paul Barry_, Mar 10 2006