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%I #14 Sep 08 2022 08:45:06
%S 6,33,165,789,3669,16725,75093,333141,1463637,6378837,27612501,
%T 118838613,508908885,2169853269,9216283989,39012619605,164640413013,
%U 692921390421,2909124515157
%N a(n) = ((6*n+19)*4^n - 1)/3.
%C Related to Collatz function (for n>0). All terms are divisible by 3.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-24,16).
%F G.f.: 3*(2-7*x+4*x^2)/((1-x)*(1-4*x)^2). - _Bruno Berselli_, Dec 16 2011
%F E.g.f.: ((19 + 24*x)*exp(4*x) - exp(x))/3. - _G. C. Greubel_, Jan 14 2020
%p seq( ((6*n+19)*4^n -1)/3, n=0..20); # _G. C. Greubel_, Jan 14 2020
%t LinearRecurrence[{9,-24,16}, {6,33,165}, 20] (* _G. C. Greubel_, Jan 14 2020 *)
%o (PARI) a(n)=((6*n+19)*4^n-1)/3 \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Magma) [((6*n+19)*4^n-1)/3: n in [0..20]]; // _G. C. Greubel_, Jan 14 2020
%o (Sage) [((6*n+19)*4^n-1)/3 for n in (0..20)] # _G. C. Greubel_, Jan 14 2020
%o (GAP) List([0..20], n-> ((6*n+19)*4^n-1)/3); # _G. C. Greubel_, Jan 14 2020
%Y Cf. A072257, A072258, A072259.
%K nonn,easy
%O 0,1
%A N. Rathankar (rathankar(AT)yahoo.com), Jul 08 2002
%E Edited and extended by _Henry Bottomley_, Aug 06 2002
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