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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 (list; graph; refs; listen; history; text; internal format)
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
Peter Lawrence et al., sequence challenge and follow-up messages on the SeqFan list, Nov 21 2011
FORMULA
G.f.: (-x^2+3*x-1)/(x^3-x^2+3*x-1).
Term (1,1) in the 3x3 matrix [0,1,0; 0,0,1; 1,-1,3]^n.
a(n) = 3*a(n-1) -a(n-2) +a(n-3) with a(0)=1, a(1)=0, a(2)=0. - Taras Goy, Jul 23 2017
MAPLE
a:= n-> (<<0|1|0>, <0|0|1>, <1|-1|3>>^n)[1, 1]:
seq(a(n), n=0..50);
CROSSREFS
Sequence in context: A048503 A318862 A318820 * A279378 A048579 A121449
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Nov 21 2011
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)