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%I #27 Mar 08 2023 08:27:58
%S 0,1,1,0,2,-1,3,-2,4,-3,5,-4,6,-5,7,-6,8,-7,9,-8,10,-9,11,-10,12,-11,
%T 13,-12,14,-13,15,-14,16,-15,17,-16,18,-17,19,-18,20,-19,21,-20,22,
%U -21,23,-22,24,-23,25,-24,26,-25,27,-26,28,-27,29,-28,30,-29,31,-30,32,-31
%N Interleave n and 1-n.
%C Partial sums are A097141. Binomial transform is x(1+x)/(1-2x), or A003945 with a leading 0.
%H Reinhard Zumkeller, <a href="/A097140/b097140.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,1,1).
%F G.f.: x*(1 + 2*x)/((1 - x)*(1 + x)^2).
%F a(n) = 3/4 + (2*n - 3)*(-1)^n/4.
%F a(0)=0, a(1)=1, a(2)=1, a(n)=a(n-1)+a(n-2)+a(n-3). - _Harvey P. Dale_, Mar 26 2012
%F G.f.: x*G(0)/(1+x) where G(k) = 1 + 2*x/(1 - x/(x + 2/G(k+1) )); (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Dec 21 2012
%F E.g.f.: ((3 + x)*sinh(x) - x*cosh(x))/2. - _Stefano Spezia_, Mar 07 2023
%t With[{nn=35},Riffle[Range[0,nn],Range[1,-(nn-1),-1]]] (* or *) LinearRecurrence[ {-1,1,1},{0,1,1},70] (* _Harvey P. Dale_, Mar 26 2012 *)
%o (Haskell)
%o import Data.List (transpose)
%o a097140 n = a097140_list !! n
%o a097140_list = concat $ transpose [a001477_list, map (1 -) a001477_list]
%o -- _Reinhard Zumkeller_, Nov 27 2012
%o (PARI) a(n)=3/4+(2*n-3)*(-1)^n/4 \\ _Charles R Greathouse IV_, Sep 02 2015
%Y Cf. A001477, A003945, A097141.
%K easy,sign
%O 0,5
%A _Paul Barry_, Jul 29 2004
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