A103750 Expansion of (1+2*x^3)/(1-x+x^3-2*x^4).

1, 1, 1, 2, 3, 4, 4, 5, 7, 11, 14, 17, 20, 28, 39, 53, 65, 82, 107, 148, 196, 253, 319, 419, 558, 745, 964, 1244, 1615, 2141, 2825, 3698, 4787, 6244, 8196, 10805, 14135, 18427, 24014, 31489, 41332, 54172, 70711, 92357, 120849, 158482, 207547, 271412, 354628, 464045

Offset: 0

Author

Roger L. Bagula, Mar 28 2005

Keywords

• nonn
• easy

Comments

Set n=4, p=2, q=-1 and r=-1 in the characteristic polynomial x^n-p*x^(n-1)+q*x+r=0.

Links

• Richard Kenyon, The Construction of Self-Similar Tilings, arXiv:math.MG/9505210
• Index entries for linear recurrences with constant coefficients, signature (1, 0, -1, 2).

Crossrefs

Cf. A099206.

Programs

Mathematica

CoefficientList[Series[(1+2x^3)/(1-x+x^3-2x^4),{x,0,50}],x] (* or *) LinearRecurrence[{1,0,-1,2},{1,1,1,2},50] (* Harvey P. Dale, Mar 30 2012 *)

Formula

a(n) = a(n-1) -a(n-3) +2*a(n-4).

Extensions

All values replaced consistent with the recurrence - the Assoc. Eds. of the OEIS - Jul 31 2010