A221949 Expansion of (-x+2*x^2-x^3-x^4-2*x^5)/(-1+3*x-2*x^2-x^4+x^5).

0, 1, 1, 2, 5, 12, 26, 53, 104, 199, 375, 700, 1299, 2402, 4432, 8167, 15038, 27677, 50925, 93686, 172337, 317000, 583078, 1072473, 1972612, 3628227, 6673379, 12274288, 22575967, 41523710, 76374044, 140473803, 258371642, 475219577, 874065113, 1607656426, 2956941213, 5438662852, 10003260594, 18398864765, 33840788320, 62242913791, 114482566991

Offset: 0

Author

N. J. A. Sloane, Feb 01 2013

Keywords

• nonn
• easy

Links

• M. Dairyko, S. Tyner, L. Pudwell and C. Wynn, Non-contiguous pattern avoidance in binary trees, 2012, arXiv:1203.0795 [math.CO], p. 18 (Class F).
• Michael Dairyko, Lara Pudwell, Samantha Tyner, Casey Wynn, Non-contiguous pattern avoidance in binary trees. Electron. J. Combin. 19 (2012), no. 3, Paper 22, 21 pp. MR2967227.
• Index entries for linear recurrences with constant coefficients, signature (3,-2,0,-1,1).

Programs

Mathematica

Join[{0},LinearRecurrence[{3,-2,0,-1,1},{1,1,2,5,12},50]] (* Harvey P. Dale, Nov 12 2014 *)
CoefficientList[Series[x*(1-2*x+x^2+x^3+2*x^4)/((1-x)^2*(1-x-x^2-x^3)) , {x, 0, 50}], x] (* Stefano Spezia, Nov 29 2018 *)

Formula

G.f.: x*(1-2*x+x^2+x^3+2*x^4)/((1-x)^2*(1-x-x^2-x^3)).