A059133 A hierarchical sequence (S(W2{2}c) - see A059126).

4, 18, 52, 126, 280, 594, 1228, 2502, 5056, 10170, 20404, 40878, 81832, 163746, 327580, 655254, 1310608, 2621322, 5242756, 10485630, 20971384, 41942898, 83885932, 167772006, 335544160, 671088474, 1342177108, 2684354382, 5368708936, 10737418050, 21474836284, 42949672758, 85899345712

Offset: 0

Author

Jonas Wallgren, Jan 19 2001

Keywords

• easy
• nonn

Links

• J. Wallgren, Hierarchical sequences
• Charlie Neder, Python program for computing A059133 and other S() sequences
• Index entries for linear recurrences with constant coefficients, signature (4, -5, 2).

Formula

Conjectures from Colin Barker, Oct 07 2015: (Start)

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

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

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

(End)

From Charlie Neder, Sep 15 2018: (Start)

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

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)

a(n) = 2*A213387(n+2). - R. J. Mathar, Apr 13 2019

Extensions

More terms via the rational g.f. - R. J. Mathar, Apr 13 2019