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%I #12 Sep 08 2022 08:45:46
%S 4,23,142,914,6016,40052,268168,1800536,12105664,81444848,548123872,
%T 3689452064,24835795456,167190009152,1125512591488,7576945713536,
%U 51008180122624,343388995528448,2311709992586752,15562542024241664
%N a(n) = ((4+sqrt(3))*(5+sqrt(3))^nv+v(4-sqrt(3))*(5-sqrt(3))^n)/2.
%C Third binomial transform of A077236. Fourth binomial transform of A162559. Fifth binomial transform of A162766.
%H Harvey P. Dale, <a href="/A162561/b162561.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, -22).
%F a(n) = 10*a(n-1) - 22*a(n-2) for n > 2; a(0) = 4, a(1) = 23.
%F G.f.: (4-17*x)/(1-10*x+22*x^2).
%t LinearRecurrence[{10,-22},{4,23},30] (* _Harvey P. Dale_, Mar 27 2013 *)
%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 14 2009
%Y Cf. A077236, A162559, A162766.
%K nonn
%O 0,1
%A Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009
%E Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 14 2009