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A059133 A hierarchical sequence (S(W2{2}c) - see A059126). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified May 24 18:34 EDT 2019. Contains 323534 sequences. (Running on oeis4.)