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A249310 Expansion of x*(1+7*x-6*x^3)/(1-8*x^2+6*x^4). 4

%I #12 Sep 22 2019 09:18:11

%S 1,7,8,50,58,358,416,2564,2980,18364,21344,131528,152872,942040,

%T 1094912,6747152,7842064,48324976,56167040,346116896,402283936,

%U 2478985312,2881269248,17755181120,20636450368,127167537088,147803987456,910809209984,1058613197440

%N Expansion of x*(1+7*x-6*x^3)/(1-8*x^2+6*x^4).

%C It seems that this is also the first row of the spectral array W(sqrt(10)-2).

%C It also seems that, for all k>0, the first row of W(sqrt(k^2+1)-k+1) has a generating function of the form x*(1+(2*k+1)*x-2*k*x^3)/(1-(2*k+2)*x^2+2*k*x^4).

%H Vincenzo Librandi, <a href="/A249310/b249310.txt">Table of n, a(n) for n = 1..1000</a>

%H A. Fraenkel and C. Kimberling, <a href="http://dx.doi.org/10.1016/0012-365X(94)90259-3">Generalized Wythoff arrays, shuffles and interspersions</a>, Discrete Mathematics 126 (1994) 137-149.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,8,0,-6).

%t CoefficientList[Series[(1 + 7 x - 6 x^3)/(1 - 8 x^2 + 6 x^4), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 25 2014 *)

%t LinearRecurrence[{0,8,0,-6},{1,7,8,50},30] (* _Harvey P. Dale_, Sep 22 2019 *)

%o (PARI) Vec((1+7*x-6*x^3)/(1-8*x^2+6*x^4) + O(x^100))

%Y Cf. A007068 (k=1), A022165 (k=2), A249311 (k=4), A249312 (k=5), A249313 (k=6).

%K nonn,easy

%O 1,2

%A _Colin Barker_, Oct 25 2014

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