A099857 Expansion of (1+3x+x^2)/(1-3x+x^2).

1, 6, 18, 48, 126, 330, 864, 2262, 5922, 15504, 40590, 106266, 278208, 728358, 1906866, 4992240, 13069854, 34217322, 89582112, 234529014, 614004930, 1607485776, 4208452398, 11017871418, 28845161856, 75517614150, 197707680594

Offset

0,2

Comments

Hankel transform is 1, -18, -36, 0, 0, 0, 0, 0, 0, 0, 0, ... - Philippe Deléham, Dec 15 2011

Links

Michael De Vlieger, Table of n, a(n) for n = 0..2391

Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.

Index entries for linear recurrences with constant coefficients, signature (3, -1).

Formula

a(n) = 0^n + 6*Fibonacci(2*n).

Mathematica

CoefficientList[Series[(1+3x+x^2)/(1-3x+x^2), {x, 0, 30}], x] (* Harvey P. Dale, May 23 2015 *)

Crossrefs

Cf. A000045, A099856, A099858.

Sequence in context: A128543 A003202 A003198 * A163765 A179754 A350155

Adjacent sequences: A099854 A099855 A099856 * A099858 A099859 A099860

Keyword

easy,nonn

Author

Paul Barry, Oct 28 2004

Status

approved