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

0,3

Comments

Binomial transform of A008611.

Links

Table of n, a(n) for n=0..30.

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

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.

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 *)

Crossrefs

Sequence in context: A351968 A097813 A167821 * A156616 A330886 A265758

Adjacent sequences: A093038 A093039 A093040 * A093042 A093043 A093044

Keyword

easy,nonn

Author

Paul Barry, Mar 18 2004

Status

approved