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%I #13 Feb 06 2022 06:20:23
%S 0,1,2,6,16,46,132,386,1136,3366,10012,29866,89256,267086,799892,
%T 2396946,7185376,21545206,64613772,193797626,581305496,1743741726,
%U 5230875652,15691927906,47074385616,141220360646,423655489532
%N Binomial transform of (Jacobsthal(n) + 2^n*Jacobsthal(-n))/2.
%C Binomial transform of Jacobsthal(n)(1-(-1)^n)/2.
%C Starting with "1" = A001045 convolved with A025192: i.e., (1, 2, 6, 16, 46, ...) = (1, 1, 3, 5, 11, ...) * (1, 2, 6, 18, 54, ...). - _Gary W. Adamson_, May 10 2013
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-1,-6).
%F G.f.: x(1-2x-x^2)/((1+x)(1-2x)(1-3x))
%F a(n) = 3^n/6 - (-1)^n/6 + 2^n/6 - 0^n/6.
%Y Cf. A001045, A094038, A051450.
%Y Cf. A025192.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Apr 23 2004
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