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%I #12 Feb 15 2021 02:00:13
%S 1,2,3,8,21,50,111,236,489,998,2019,4064,8157,16346,32727,65492,
%T 131025,262094,524235,1048520,2097093,4194242,8388543,16777148,
%U 33554361,67108790,134217651,268435376,536870829
%N Row sums of triangle A132729.
%H G. C. Greubel, <a href="/A132730/b132730.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 (4,-5,2).
%F Binomial transform of [1, 1, 0, 4, 0, 4, 0, 4, ...].
%F a(n) = 2^(n+1) - 3*n + 1, for n > 0. - _R. J. Mathar_, Apr 04 2012
%F From _G. C. Greubel_, Feb 14 2021: (Start)
%F G.f.: (1 - 2*x + 4*x^3)/((1-x)^2 * (1-2*x)).
%F E.g.f.: -2 + (1-3*x)*exp(x) + 2*exp(2*x). (End)
%e a(4) = 21 = sum of row 4 terms of triangle A132729: (1 + 5 + 9 + 5 + 1).
%e a(3) = 8 = (1, 3, 3, 1) dot (1, 1, 0, 4) = (1 + 3 + 0 + 4).
%t LinearRecurrence[{4,-5,2},{1,2,3,8},30] (* _Harvey P. Dale_, Dec 30 2015 *)
%t Table[2^(n+1) -3*n +1 -2*Boole[n==0], {n,0,30}] (* _G. C. Greubel_, Feb 14 2021 *)
%o (Sage) [1]+[2^(n+1) -3*n +1 for n in (1..30)] # _G. C. Greubel_, Feb 14 2021
%o (Magma) [1] cat [2^(n+1) -3*n +1: n in [0..30]]; // _G. C. Greubel_, Feb 14 2021
%Y Cf. A132729.
%K nonn,easy
%O 0,2
%A _Gary W. Adamson_, Aug 26 2007
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