A093041 Expansion of (1-4x+6x^2-3x^3)/(1-5x+9x^2-8x^3+4x^4).

1, 1, 2, 6, 16, 38, 86, 192, 426, 938, 2048, 4438, 9558, 20480, 43690, 92842, 196608, 415062, 873814, 1835008, 3844778, 8039082, 16777216, 34952534, 72701270, 150994944, 313174698, 648719018, 1342177280, 2773833046, 5726623062

Offset: 0

Author

Paul Barry, Mar 18 2004

Keywords

• easy
• nonn

Comments

Binomial transform of A008611.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-9,8,-4)

Programs

Mathematica

CoefficientList[Series[(1-4x+6x^2-3x^3)/(1-5x+9x^2-8x^3+4x^4),{x,0,30}],x] (* or *) LinearRecurrence[ {5,-9,8,-4},{1,1,2,6},40] (* Harvey P. Dale, Feb 27 2024 *)

Formula

a(n)=2(cos(pi*n/3)-sqrt(3)sin(pi*n/3)/3)/3+2^n/3+n*2^(n-1)/3; a(n)=2*A010892(n+1)/3+A000079(n)/3+A001787(n)/3.