A120771 Expansion of ( 1-x^3+x^4+x^5-x^8 ) / ( 1-2*x^3-x^6+x^9 ).

1, 0, 0, 1, 1, 1, 3, 2, 1, 6, 5, 3, 14, 11, 6, 31, 25, 14, 70, 56, 31, 157, 126, 70, 353, 283, 157, 793, 636, 353, 1782, 1429, 793, 4004, 3211, 1782, 8997, 7215, 4004, 20216, 16212, 8997, 45425, 36428, 20216, 102069, 81853, 45425, 229347, 183922, 102069, 515338, 413269, 229347, 1157954, 928607, 515338

Offset: 0

Author

Gary W. Adamson, Jul 03 2006

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,1,0,0,-1).

Crossrefs

Cf. A077998 (trisection), A006054 (trisection), A006356 (trisection), A038196.

Programs

Mathematica

CoefficientList[Series[(1-x^3+x^4+x^5-x^8)/(1-2*x^3-x^6+x^9),{x,0,60}],x] (* or *) LinearRecurrence[{0,0,2,0,0,1,0,0,-1},{1,0,0,1,1,1,3,2,1},60] (* Harvey P. Dale, Feb 19 2016 *)

Formula

Three consecutive coefficients are generated from the left row of the n-th power of the matrix [1,1,1; 1,1,0; 1,0,0].