A098179 Expansion of (1-3*x+3*x^2)/(1-5*x+10*x^2-10*x^3+4*x^4).

1, 2, 3, 5, 11, 27, 63, 135, 271, 527, 1023, 2015, 4031, 8127, 16383, 32895, 65791, 131327, 262143, 523775, 1047551, 2096127, 4194303, 8390655, 16781311, 33558527, 67108863, 134209535, 268419071, 536854527, 1073741823, 2147516415

Offset: 0

Author

Paul Barry, Aug 30 2004

Keywords

• easy
• nonn

Comments

Partial sums of A038503. Binomial transform of A098178.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-4).

Programs

Mathematica

LinearRecurrence[{5,-10,10,-4},{1,2,3,5},40] (* or *) CoefficientList[ Series[(1-3 x+3 x^2)/(1-5 x+10 x^2-10 x^3+4 x^4),{x,0,40}],x] (* Harvey P. Dale, Oct 06 2011 *)

Formula

a(n) = 2^n+2^(n/2)cos(pi*n/4)-1; a(n) = 5a(n-1)-10a(n-2)+10a(n-3)-4a(n-4).