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%I #23 Sep 08 2022 08:45:40
%S 1,2,4,8,17,38,87,200,457,1034,2315,5132,11277,24590,53263,114704,
%T 245777,524306,1114131,2359316,4980757,10485782,22020119,46137368,
%U 96469017,201326618,419430427,872415260,1811939357,3758096414,7784628255,16106127392,33285996577
%N Row sums of number triangle A154221.
%H G. C. Greubel, <a href="/A154222/b154222.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4).
%F a(n) = (1/4)*( 4*(n+1) + (n-1)*2^n + 0^n).
%F From _Colin Barker_, Oct 11 2014: (Start)
%F a(n) = A045618(n-4) + 2^n for n>3.
%F a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n>4.
%F a(n) = (4 - 2^n + (4+2^n)*n)/4 for n>0.
%F G.f.: (x^4 - 2*x^3 + 5*x^2 - 4*x + 1) / ((x-1)^2*(2*x-1)^2).
%F (End)
%F E.g.f.: (1/4)*(1 + 4*(1 + x)*exp(x) + (2*x - 1)*exp(2*x)). - _G. C. Greubel_, Sep 06 2016
%t Join[{1},LinearRecurrence[{6, -13, 12, -4}, {2, 4, 8,17}, 25]] (* or *) Table[(1/4)*( 4*(n+1) + (n-1)*2^n + 0^n), {n,0,25}] (* _G. C. Greubel_, Sep 06 2016 *)
%o (PARI) Vec((x^4-2*x^3+5*x^2-4*x+1)/((x-1)^2*(2*x-1)^2) + O(x^100)) \\ _Colin Barker_, Oct 11 2014
%o (Magma) [(1/4)*(4*(n+1)+(n-1)*2^n+0^n): n in [0..35]]; // _Vincenzo Librandi_, Sep 07 2016
%Y Cf. A045618, A154221.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jan 05 2009
%E More terms and xrefs from _Colin Barker_, Oct 11 2014
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