

A200752


Expansion of (x^2 + 3*x  1)/(x^3  x^2 + 3*x  1).


3



1, 0, 0, 1, 3, 8, 22, 61, 169, 468, 1296, 3589, 9939, 27524, 76222, 211081, 584545, 1618776, 4482864, 12414361, 34378995, 95205488, 263651830, 730128997, 2021940649, 5599344780, 15506222688, 42941263933, 118916913891, 329315700428, 911971451326, 2525515567441
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OFFSET

0,5


COMMENTS

Peter A. Lawrence (see links) has posted a challenge to find a 3x3 integer matrix with "smallish" elements whose powers generate a sequence that is not in the OEIS. This sequence is one of the solutions found.
a(n+3) is the number of ternary strings of length n in which the number of substrings of the form 0011 equals the number of substrings of the form 11.  John M. Campbell, Nov 02 2013


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..700
Peter Lawrence et al., sequence challenge and followup messages on the SeqFan list, Nov 21 2011
Index entries for linear recurrences with constant coefficients, signature (3,1,1)


FORMULA

G.f.: (x^2+3*x1)/(x^3x^2+3*x1).
Term (1,1) in the 3x3 matrix [0,1,0; 0,0,1; 1,1,3]^n.
a(n) = 3*a(n1) a(n2) +a(n3) with a(0)=1, a(1)=0, a(2)=0.  Taras Goy, Jul 23 2017


MAPLE

a:= n> (<<010>, <001>, <113>>^n)[1, 1]:
seq(a(n), n=0..50);


CROSSREFS

Cf. A200676, A200739, A200715.
Sequence in context: A255705 A014397 A048503 * A279378 A048579 A121449
Adjacent sequences: A200749 A200750 A200751 * A200753 A200754 A200755


KEYWORD

nonn,easy


AUTHOR

Alois P. Heinz, Nov 21 2011


STATUS

approved



