A173652 Expansion of g.f.: x^3*(1 + 4*x - x^2 - 6*x^3 + x^4)/(1 - 9*x^2 - 3*x^3 + 17*x^4 + 8*x^5 - 6*x^6 - 7*x^7 + x^8 - x^9).

0, 0, 0, 1, 4, 8, 33, 68, 245, 549, 1815, 4331, 13524, 33766, 101383, 261293, 763745, 2011959, 5774140, 15440569, 43764595, 118231475, 332290914, 903952326, 2526016085, 6904206021, 19218113777, 52696460176, 146294791786, 402018135352, 1114070627578

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,9,3,-17,-8,6,7,-1,1).

Mathematica

M =  {{0, 1, 0, 1, 0, 0, 0, 0, 0},
      {0, 0, 1, 0, 1, 0, 0, 0, 0},
      {1, 1, 0, 0, 0, 1, 0, 0, 0},
      {1, 0, 0, 0, 0, 1, 1, 0, 0},
      {0, 1, 0, 1, 0, 1, 0, 1, 0},
      {0, 0, 1, 0, 1, 0, 0, 0, 1},
      {0, 0, 0, 1, 0, 0, 0, 1, 0},
      {0, 0, 0, 0, 1, 0, 0, 0, 1},
      {0, 0, 0, 0, 0, 1, 1, 1, 0}};
v[0]= {0, 0, 0, 0, 0, 0, 0, 0, 1};
v[n_] := v[n] = M.v[n - 1]
Table[v[n][[1]], {n, 0, 30}] (* or *)
LinearRecurrence[{0, 9, 3, -17, -8, 6, 7, -1, 1}, {0, 0, 0, 1, 4, 8, 33, 68, 245}, 31] (* Georg Fischer, May 03 2019 *)
CoefficientList[Series[x^3*(1+4*x-x^2-6*x^3+x^4)/(1-9*x^2-3*x^3+17*x^4 + 8*x^5-6*x^6-7*x^7+x^8-x^9), {x, 0, 30}], x] (* G. C. Greubel, May 03 2019 *)

Prog

(PARI) my(x='x+O('x^30)); concat([0, 0, 0], Vec(x^3*(1+4*x-x^2-6*x^3+x^4)/( 1-9*x^2-3*x^3+17*x^4+8*x^5-6*x^6-7*x^7+x^8-x^9))) \\ G. C. Greubel, May 03 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0, 0, 0] cat Coefficients(R!( x^3*(1+4*x-x^2-6*x^3+x^4)/( 1-9*x^2-3*x^3+17*x^4+8*x^5 -6*x^6-7*x^7+x^8-x^9) )); // G. C. Greubel, May 03 2019
(Sage) (x^3*(1+4*x-x^2-6*x^3+x^4)/( 1-9*x^2-3*x^3 +17*x^4+8*x^5-6*x^6 -7*x^7+x^8-x^9)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 03 2019

Crossrefs

Cf. A000931.

Sequence in context: A032467 A009265 A173326 * A149095 A149096 A149097

Adjacent sequences: A173649 A173650 A173651 * A173653 A173654 A173655

Keyword

nonn,easy,less

Author

Roger L. Bagula, Nov 24 2010

Extensions

Definition corrected by Georg Fischer, May 03 2019

Status

approved