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A132736 Row sums of triangle A132735.

%I A132736 #14 Feb 14 2021 18:39:37
%S A132736 1,2,5,10,19,36,69,134,263,520,1033,2058,4107,8204,16397,32782,65551,
%T A132736 131088,262161,524306,1048595,2097172,4194325,8388630,16777239,
%U A132736 33554456,67108889,134217754,268435483,536870940,1073741853,2147483678
%N A132736 Row sums of triangle A132735.
%C A132736 Apart from first term, the same as A052944. - _R. J. Mathar_, Jun 12 2008
%H A132736 G. C. Greubel, <a href="/A132736/b132736.txt">Table of n, a(n) for n = 0..1000</a>
%H A132736 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A132736 Binomial transform of [1, 1, 2, 0, 2, 0, 2, 0, 2, ...].
%F A132736 From _Colin Barker_, Aug 12 2012: (Start)
%F A132736 a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3) for n>3.
%F A132736 G.f.: (1 -2*x +2*x^2 -2*x^3)/((1-x)^2*(1-2*x)). (End)
%F A132736 From _G. C. Greubel_, Feb 14 2021: (Start)
%F A132736 a(n) = 2^n + n - 1 + [n=0].
%F A132736 E.g.f.: 1 - (1-x)*exp(x) + exp(2*x). (End)
%e A132736 a(4) = 19 = sum of row 4 terms of triangle A132735: (1 + 5 + 7 + 5 + 1).
%e A132736 a(3) = 10 = (1, 3, 3, 1) dot (1, 1, 2, 0) = (1 + 3 + 6 + 0).
%p A132736 a:= proc(n) option remember; if n=0 then 1 else add((binomial(n,j)+1), j=0..n-1) fi end: seq(a(n), n=0..31);# _Zerinvary Lajos_, Mar 29 2009
%t A132736 Table[2^n + n-1 + Boole[n==0], {n,0,30}] (* _G. C. Greubel_, Feb 14 2021 *)
%o A132736 (Sage) [1]+[2^n + n-1 for n in (1..30)] # _G. C. Greubel_, Feb 14 2021
%o A132736 (Magma) [1] cat [2^n + n-1: n in [1..30]]; // _G. C. Greubel_, Feb 14 2021
%Y A132736 Cf. A132735.
%K A132736 nonn
%O A132736 0,2
%A A132736 _Gary W. Adamson_, Aug 26 2007
%E A132736 More terms from _R. J. Mathar_, Jun 12 2008