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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

Alois P. Heinz, Table of n, a(n) for n = 0..700

Peter Lawrence et al., sequence challenge and follow-up 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*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

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

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Last modified November 18 09:09 EST 2017. Contains 294879 sequences.