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

%I #21 Oct 01 2023 18:25:02

%S 1,6,18,48,126,330,864,2262,5922,15504,40590,106266,278208,728358,

%T 1906866,4992240,13069854,34217322,89582112,234529014,614004930,

%U 1607485776,4208452398,11017871418,28845161856,75517614150,197707680594

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

%C Hankel transform is 1, -18, -36, 0, 0, 0, 0, 0, 0, 0, 0, ... - _Philippe Deléham_, Dec 15 2011

%H Michael De Vlieger, <a href="/A099857/b099857.txt">Table of n, a(n) for n = 0..2391</a>

%H Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Nemeth/nemeth7.html">Ellipse Chains and Associated Sequences</a>, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3, -1).

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

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

%Y Cf. A000045, A099856, A099858.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Oct 28 2004