A108153 a(n) = 3*a(n-1) + 2*a(n-2) + a(n-3).
0, 1, 3, 11, 40, 145, 526, 1908, 6921, 25105, 91065, 330326, 1198213, 4346356, 15765820, 57188385, 207443151, 752472043, 2729490816, 9900859685, 35914032730, 130273308376, 472548850273, 1714107200301, 6217692609825, 22553841080350, 81811015661001
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (3,2,1).
Programs
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Mathematica
M = {{0, 1, 0}, {0, 0, 1}, {1, 2, 3}} a3 = Table[MatrixPower[M, i][[1, 3]], {i, 1, 50}] LinearRecurrence[{3,2,1},{0,1,3},40] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2012 *) nxt[{a_,b_,c_}]:={b,c,a+2b+3c}; NestList[nxt,{0,1,3},30][[;;,1]] (* Harvey P. Dale, Nov 22 2024 *)
Formula
G.f.: x/(1-3*x-2*x^2-x^3). [R. J. Mathar, Mar 19 2009]
a(n) = 11*a(n-2) +7*a(n-3)+3*a(n-4). [Gary Detlefs, Sep 13 2010]
Extensions
Definition replaced by the Adamson recurrence - the Associate Editors of the OEIS, Sep 28 2009