A133931 Expansion of x*(2-4*x^2-x^3)/((1-x)^2*(1-x-x^2)).

2, 6, 10, 15, 21, 29, 40, 56, 80, 117, 175, 267, 414, 650, 1030, 1643, 2633, 4233, 6820, 11004, 17772, 28721, 46435, 75095, 121466, 196494, 317890, 514311, 832125, 1346357, 2178400, 3524672, 5702984, 9227565, 14930455, 24157923, 39088278

Offset

1,1

Links

Table of n, a(n) for n=1..37.

Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).

Formula

a(n) = 3*a(n-1)-2*a(n-2)-a(n-3)+a(n-4). G.f.: x*(2-4*x^2-x^3)/((1-x)^2*(1-x-x^2)). [Colin Barker, Jun 10 2012]

Mathematica

M = {{0, 1, 0, 0}, {1, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 3, 1}}; v[1] = {0, 1, 1, 0}; v[n_] := v[n] = M.v[n - 1] a = Table[Apply[Plus, v[n]], {n, 1, 50}]
Rest[CoefficientList[Series[x (2-4x^2-x^3)/((1-x)^2(1-x-x^2)), {x, 0, 40}], x]] (* or *) LinearRecurrence[{3, -2, -1, 1}, {2, 6, 10, 15}, 40] (* Harvey P. Dale, Jan 04 2013 *)

Crossrefs

Sequence in context: A343148 A331250 A186783 * A050895 A184426 A293408

Adjacent sequences: A133928 A133929 A133930 * A133932 A133933 A133934

Keyword

nonn,easy

Author

Roger L. Bagula, Jan 08 2008

Extensions

New name from Colin Barker and Joerg Arndt, Jun 10 2012

Status

approved