A174191 Expansion of (1+x)*(2*x-1)/((1-x)*(x^2+2*x-1)).
1, 2, 3, 6, 13, 30, 71, 170, 409, 986, 2379, 5742, 13861, 33462, 80783, 195026, 470833, 1136690, 2744211, 6625110, 15994429, 38613966, 93222359, 225058682, 543339721, 1311738122, 3166815963, 7645370046, 18457556053, 44560482150, 107578520351
Offset: 0
Keywords
Examples
a(2) = 2*a(1) + a(0) - 2 = 2*2 + 1 - 2 = 3 a(3) = 2*a(2) + a(1) - 2 = 2*3 + 2 - 2 = 6.
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-1,-1).
Programs
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Mathematica
LinearRecurrence[{3, -1, -1}, {1, 2, 3}, 31] (* Robert P. P. McKone, Apr 03 2022 *)
Formula
a(n) = 2*a(n-1) + a(n-2) - 2, with a(0)=1, a(1)=2.
From R. J. Mathar, Mar 17 2010: (Start)
a(n) = A052937(n-1), n > 0.
a(n) = 3*a(n-1) - a(n-2) - a(n-3). (End)
Comments