A059133 - OEIS

%I #26 Jul 02 2023 15:52:44

%S 4,18,52,126,280,594,1228,2502,5056,10170,20404,40878,81832,163746,

%T 327580,655254,1310608,2621322,5242756,10485630,20971384,41942898,

%U 83885932,167772006,335544160,671088474,1342177108,2684354382,5368708936,10737418050,21474836284,42949672758,85899345712

%N A hierarchical sequence (S(W2{2}c) - see A059126).

%H J. Wallgren, <a href="/A059126/a059126.txt">Hierarchical sequences</a>

%H Charlie Neder, <a href="/A059133/a059133.txt">Python program for computing A059133 and other S() sequences</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4, -5, 2).

%F Conjectures from _Colin Barker_, Oct 07 2015: (Start)

%F a(n) = 4*(-4+5*2^n)-6*n.

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

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

%F (End)

%F From _Charlie Neder_, Sep 15 2018: (Start)

%F a(1) is the sum of the first phrase, (1,2,1).

%F W2{2}c can be generated by starting with (1,2,1) as W(1) and repeatedly applying W(n) = W(n-1) + (2n-1,2n,2n-1) + W(n-1), which implies a(n) = 2*a(n-1) + 6n - 2, from which the formulas follow. (End)

%F a(n) = 2*A213387(n+2). - _R. J. Mathar_, Apr 13 2019

%K easy,nonn

%O 0,1

%A _Jonas Wallgren_, Jan 19 2001

%E More terms via the rational g.f. - _R. J. Mathar_, Apr 13 2019