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A101945 a(n) = 6*2^n - n - 5.

%I A101945 #21 Feb 06 2022 10:06:37
%S A101945 1,6,17,40,87,182,373,756,1523,3058,6129,12272,24559,49134,98285,
%T A101945 196588,393195,786410,1572841,3145704,6291431,12582886,25165797,
%U A101945 50331620,100663267,201326562,402653153,805306336,1610612703,3221225438
%N A101945 a(n) = 6*2^n - n - 5.
%H A101945 G. C. Greubel, <a href="/A101945/b101945.txt">Table of n, a(n) for n = 0..1000</a>
%H A101945 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A101945 a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n >= 3.
%F A101945 Row sums of triangle A135855. - _Gary W. Adamson_, Dec 01 2007
%F A101945 From _G. C. Greubel_, Feb 06 2022: (Start)
%F A101945 G.f.: (1 + 2*x - 2*x^2)/((1-x)^2*(1-2*x)).
%F A101945 E.g.f.: 6*exp(2*x) - (5+x)*exp(x). (End)
%t A101945 a[0]=1; a[1]=6; a[2]=17; a[n_]:= a[n]= 4a[n-1] -5a[n-2] +2a[n-3];
%t A101945 Table[a[n], {n, 0, 30}] (* _Robert G. Wilson v_, Jan 12 2005 *)
%o A101945 (PARI) a(n)=if(n==1,1,if(n==2,6,if(n==3,17,4*a(n-1)-5*a(n-2)+2*a(n-3)))) \\ (Klasen)
%o A101945 (Magma) [6*2^n -n-5: n in [0..40]]; // _G. C. Greubel_, Feb 06 2022
%o A101945 (Sage) [3*2^(n+1) -(n+5) for n in (0..40)] # _G. C. Greubel_, Feb 06 2022
%Y A101945 Cf. A033484, A101946, A135855.
%K A101945 nonn,easy
%O A101945 0,2
%A A101945 _Gary W. Adamson_, Dec 22 2004
%E A101945 More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jan 06 2005
%E A101945 New definition from _Ralf Stephan_, May 17 2007