A200752 Expansion of (-x^2 + 3*x - 1)/(x^3 - x^2 + 3*x - 1).
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
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..2263
- 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)
Programs
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Maple
a:= n-> (<<0|1|0>, <0|0|1>, <1|-1|3>>^n)[1, 1]: seq(a(n), n=0..50);
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
Comments