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%I #30 Aug 22 2015 11:16:17
%S 3,9,30,108,408,1584,6240,24768,98688,393984,1574400,6294528,25171968,
%T 100675584,402677760,1610661888,6442549248,25770000384,103079608320,
%U 412317646848,1649269014528,6597072912384,26388285358080,105553128849408
%N "BIK" (reversible, indistinct, unlabeled) transform of 3,3,3,3...
%C Number of solutions (x,y,z) to x+y+z = 2^n, x>=0, y>=0, z>=0, gcd(x,y,z)=1. - _Vladeta Jovovic_, Dec 22 2002
%H Harvey P. Dale, <a href="/A032125/b032125.txt">Table of n, a(n) for n = 1..1000</a>
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-8)
%F a(n) = 3*2^(n-2)*(2^(n-1)+1). - _Vladeta Jovovic_, Dec 22 2002
%F Binomial transform of A067771 (if the offset is changed to 0). - _Carl Najafi_, Sep 09 2011
%F G.f. -3*x*(-1+3*x) / ( (4*x-1)*(2*x-1) ). a(n)=3*A007582(n-1). - _R. J. Mathar_, Sep 11 2011
%F a(1)=3, a(2)=9, a(n) = 6*a(n-1)-8*a(n-2). [_Harvey P. Dale_, Jan 01 2012]
%F E.g.f.: (3/8)*(exp(4*x) + 2*exp(2*x) - 3). - _G. C. Greubel_, Aug 22 2015
%t Table[3*2^(n-2)(2^(n-1)+1),{n,30}] (* or *) LinearRecurrence[{6,-8},{3,9},30] (* _Harvey P. Dale_, Jan 01 2012 *)
%t RecurrenceTable[{a[0]== 3, a[1]== 9, a[n]== 6*a[n-1] - 8*a[n-2]}, a, {n,50}] (* _G. C. Greubel_, Aug 22 2015 *)
%Y a(n) = A048240(2^n).
%K nonn,easy
%O 1,1
%A _Christian G. Bower_
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