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A132753 a(n) = 2^(n+1) - n + 1.

%I A132753 #30 Mar 06 2022 00:20:16
%S A132753 3,4,7,14,29,60,123,250,505,1016,2039,4086,8181,16372,32755,65522,
%T A132753 131057,262128,524271,1048558,2097133,4194284,8388587,16777194,
%U A132753 33554409,67108840,134217703,268435430,536870885,1073741796,2147483619
%N A132753 a(n) = 2^(n+1) - n + 1.
%C A132753 Apart from a(0): Row sums of triangle A132752 (old name).
%C A132753 Apart from a(0): Binomial transform of [1, 3, 0, 4, 0, 4, 0, 4, ...].
%H A132753 G. C. Greubel, <a href="/A132753/b132753.txt">Table of n, a(n) for n = 0..1000</a>
%H A132753 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A132753 From _Colin Barker_, Mar 14 2014: (Start)
%F A132753 a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
%F A132753 G.f.: (3 - 8*x + 6*x^2)/((1-x)^2 * (1-2*x)). (End)
%F A132753 E.g.f.: (1-x)*exp(x) + 2*exp(2*x). - _G. C. Greubel_, Feb 16 2021
%e A132753 a(3) = 14 = sum of row 3 terms of triangle A132752: (3 + 5 + 5 + 1).
%e A132753 a(3) = 14 = (1, 3, 3, 1) dot (1, 3, 0, 4) = (1 + 9 + 0 + 4).
%p A132753 A132753:= n-> 2^(n+1) -n+1; seq(A132753(n), n=0..40) # _G. C. Greubel_, Feb 16 2021
%t A132753 Table[2^(n+1) -n+1, {n, 0, 30}] (* _Bruno Berselli_, Aug 31 2013 *)
%o A132753 (PARI) a(n)=2^(n+1)-n+1
%o A132753 (PARI) Vec( (3-8*x+6*x^2)/((1-x)^2*(1-2*x)) + O(x^40)) \\ _Colin Barker_, Mar 14 2014
%o A132753 (Sage) [2^(n+1) -n+1 for n in (0..40)] # _G. C. Greubel_, Feb 16 2021
%o A132753 (Magma) [2^(n+1) -n+1: n in [0..40]]; // _G. C. Greubel_, Feb 16 2021
%Y A132753 Cf. A132752.
%Y A132753 Cf. A003462, A007051, A024023, A029858, A034472, A052548, A058481, A067771, A079004, A100774, A115099, A134931. - _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008
%K A132753 nonn,easy
%O A132753 0,1
%A A132753 _Gary W. Adamson_, Aug 28 2007
%E A132753 More terms _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008
%E A132753 Changed first member, and better name from _Ralf Stephan_, Aug 31 2013