OFFSET
0,1
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
CROSSREFS
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