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A133095 Row sums of triangle A133094.

%I A133095 #16 Sep 08 2022 08:45:31
%S A133095 1,4,9,20,43,90,185,376,759,1526,3061,6132,12275,24562,49137,98288,
%T A133095 196591,393198,786413,1572844,3145707,6291434,12582889,25165800,
%U A133095 50331623,100663270,201326565,402653156,805306339,1610612706,3221225441,6442450912,12884901855,25769803742,51539607517
%N A133095 Row sums of triangle A133094.
%H A133095 G. C. Greubel, <a href="/A133095/b133095.txt">Table of n, a(n) for n = 1..1000</a>
%H A133095 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A133095 Binomial transform of [1, 3, 2, 4, 2, 4, 2, 4, ...].
%F A133095 From _G. C. Greubel_, Oct 21 2017: (Start)
%F A133095 a(n) = 3*2^(n-1) - n, for n >= 2.
%F A133095 a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
%F A133095 G.f.: x*(1 - 2*x^2 + 2*x^3)/((1-2*x)*(1-x)^2).
%F A133095 E.g.f.: (3*exp(2*x) - 2*x*exp(x) - 2*x - 3)/2. (End)
%F A133095 a(n) = A123720(n) for n >= 2. - _Georg Fischer_, Nov 02 2018
%e A133095 a(4) = 20 = sum of row 4 terms of triangle A133094: (7 + 7 + 5 + 1).
%e A133095 a(4) = 20 = (1, 3, 3, 1) dot (1, 3, 2, 4) = (1 + 9 + 6 + 4).
%t A133095 Join[{1}, Table[ 3*2^(n - 1) - n, {n, 2, 50}]] (* _G. C. Greubel_, Oct 21 2017 *)
%t A133095 LinearRecurrence[{4,-5,2},{1,4,9,20},50] (* _Harvey P. Dale_, Aug 09 2022 *)
%o A133095 (PARI) concat(1, for(n=1,50, print1(3*2^(n - 1) - n, ", "))) \\ _G. C. Greubel_, Oct 21 2017
%o A133095 (Magma) [1] cat [3*2^(n - 1) - n: n in [2..50]]; // _G. C. Greubel_, Oct 21 2017
%Y A133095 Cf. A123720, A133094.
%K A133095 nonn
%O A133095 1,2
%A A133095 _Gary W. Adamson_, Sep 09 2007
%E A133095 Terms a(11) onward added by _G. C. Greubel_, Oct 21 2017