%I #26 Mar 06 2022 00:20:32

%S 1,2,7,16,33,66,131,260,517,1030,2055,4104,8201,16394,32779,65548,

%T 131085,262158,524303,1048592,2097169,4194322,8388627,16777236,

%U 33554453,67108886,134217751,268435480,536870937,1073741850,2147483675,4294967324,8589934621

%N Row sums of triangle A132737.

%H Vincenzo Librandi, <a href="/A132738/b132738.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, 4, 0, 4, 0, 4, ...].

%F a(n) = 2^(n+1) + n - 3 for n > 0. - _Franklin T. Adams-Watters_, Jul 06 2009

%F From _Colin Barker_, Mar 14 2014: (Start)

%F a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n>3.

%F G.f.: (1 -2*x +4*x^2 -4*x^3)/((1-x)^2*(1-2*x)). (End)

%F E.g.f.: 2 - (3-x)*exp(x) + 2*exp(2*x). - _G. C. Greubel_, Feb 15 2021

%e a(3) = 16 = sum of row 3 terms of triangle A132737: (1 + 7 + 7 + 1).

%e a(3) = 16 = (1, 3, 3, 1) dot (1, 1, 4, 0) = (1 + 3 + 12 + 0).

%t Join[{1,2,7}, Table[BitSet[n, (n+4)], {n,0,40}]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 19 2011 *)

%t Table[2^(n+1) +n-3 +2*Boole[n==0], {n,0,40}] (* _G. C. Greubel_, Feb 15 2021 *)

%o (PARI) Vec((1-2*x+4*x^2-4*x^3)/((1-x)^2*(1-2*x)) + O(x^40)) \\ _Colin Barker_, Mar 14 2014

%o (Sage) [1]+[2^(n+1) +n-3 for n in (1..40)] # _G. C. Greubel_, Feb 15 2021

%o (Magma) [1] cat [2^(n+1) +n-3: n in [1..40]]; // _G. C. Greubel_, Feb 15 2021

%Y Cf. A132737.

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Aug 26 2007

%E Extended by _Franklin T. Adams-Watters_, Jul 06 2009