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Sum of odd numbers starting with 1, alternating signs (beginning with plus)
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%I #42 Feb 08 2016 12:05:36

%S 1,4,-1,6,-3,8,-5,10,-7,12,-9,14,-11,16,-13,18,-15,20,-17,22,-19,24,

%T -21,26,-23,28,-25,30,-27,32,-29,34,-31,36,-33,38,-35,40,-37,42,-39,

%U 44,-41,46,-43,48,-45,50,-47,52,-49

%N Sum of odd numbers starting with 1, alternating signs (beginning with plus)

%C 1st,3rd,5th (odd terms) increase by 2, 2nd,4th,6th,8th (even terms) decrease by 2 each time.

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

%F a(n) = -a(n-1) + a(n-2) + a(n-3). - _Charles R Greathouse IV_, Aug 02 2013

%F G.f.: x*(2*x^2 + 5*x + 1)/((1-x)*(1+x)^2). a(n) = n*(-1)^n + 2 = A038608(n) + 2. - _Ralf Stephan_, Aug 07 2013

%e (1+3)=4 (4-5)=-1 (-1+7)=6 (6-9)=-3 (-3+11)=8 (8-13)=-5 (-5+15)=10.

%o (PARI) a(n) = n*(-1)^n + 2; \\ _Michel Marcus_, Feb 08 2016

%Y Cf. A065164 (absolute values).

%K sign,easy

%O 1,2

%A _D.Wilde_, Aug 02 2013