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%I #24 Mar 09 2024 12:58:13
%S 1,5,19,66,216,679,2075,6211,18299,53244,153366,438095,1242709,
%T 3504161,9830371,27454614,76375860,211732471,585157679,1612689439,
%U 4433421131,12160156560,33284285874,90931830431
%N Main diagonal of the array A059503.
%H G. C. Greubel, <a href="/A059509/b059509.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6,-1).
%F From _Colin Barker_, Nov 30 2012: (Start)
%F a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).
%F G.f.: x*(x^3-x+1)/(x^2-3*x+1)^2. (End)
%F a(n) = ((3 - n)*Fibonacci(2*n) - (5 - 8*n)*Fibonacci(2*n - 1))/5. - _G. C. Greubel_, Sep 10 2017
%t Rest[CoefficientList[Series[x*(x^3 - x + 1)/(x^2 - 3*x + 1)^2, {x,0,50}], x]] (* or *) Table[((3 - n)*Fibonacci[2*n] - (5 - 8*n)*Fibonacci[2*n - 1])/5, {n, 1, 50}] (* _G. C. Greubel_, Sep 10 2017 *)
%o (PARI) Vec(x*(x^3-x+1)/(x^2-3*x+1)^2 + O(x^40)) \\ _Michel Marcus_, Sep 09 2017
%Y Cf. A059503.
%K easy,nonn
%O 1,2
%A _Floor van Lamoen_, Jan 19 2001
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