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%I #21 Sep 26 2017 16:25:08
%S 1,1,2,4,9,17,34,68,137,273,546,1092,2185,4369,8738,17476,34953,69905,
%T 139810,279620,559241,1118481,2236962,4473924,8947849,17895697,
%U 35791394,71582788,143165577,286331153,572662306,1145324612,2290649225,4581298449,9162596898
%N Expansion of 1/((1+x)*(1-2*x)*(1+x^2)).
%C Signed version is A077931. Row sums of A115450.
%H G. C. Greubel, <a href="/A115451/b115451.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec$order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,2).
%F a(n) = a(n-1) + a(n-2) + a(n-3) + 2*a(n-4);
%F a(n) = Sum_{k=0..n} (2^(n-k+1)-1)(-1)^k} - Sum_{k=0..floor(n/2)} (2^(n-2k)-1)(-1)^k}.
%F a(n) = A000975(n+1) - A077854(n-1).
%F a(n) = A112030(n)/10 + (-1)^n/6 +2^(n+3)/15. - _R. J. Mathar_, Feb 06 2011
%t CoefficientList[Series[1/((1 + x) (1 - 2 x) (1 + x^2)), {x, 0, 50}], x] (* _Vladimir Joseph Stephan Orlovsky_, Jun 20 2011 *)
%t LinearRecurrence[{1,1,1,2},{1,1,2,4},50] (* _Harvey P. Dale_, Oct 22 2011 *)
%o (PARI) x='x+O('x^50); Vec(1/((1+x)*(1-2*x)*(1+x^2))) \\ _G. C. Greubel_, Sep 26 2017
%K easy,nonn
%O 0,3
%A _Paul Barry_, Jan 22 2006
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