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

0,1

Links

Table of n, a(n) for n=0..32.

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

Crossrefs

Sequence in context: A225263 A092349 A027659 * A300493 A300876 A301486

Adjacent sequences: A059130 A059131 A059132 * A059134 A059135 A059136

Keyword

easy,nonn

Author

Jonas Wallgren, Jan 19 2001

Extensions

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

Status

approved