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%I #12 Sep 08 2022 08:45:06
%S 0,9,69,405,2133,10581,50517,234837,1070421,4805973,21321045,93672789,
%T 408245589,1767200085,7605671253,32570168661,138870609237,
%U 589842175317,2496807654741,10536986432853
%N a(n) = ((6*n+1)*4^n - 1)/3.
%C Related to Collatz function (for n>0). All divisible by 3.
%H G. C. Greubel, <a href="/A072258/b072258.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-24,16).
%F G.f.: 3*x*(3-4*x)/((1-x)*(1-4*x)^2). - _Bruno Berselli_, Dec 16 2011
%F E.g.f.: ( (1 + 24*x)*exp(4*x) - exp(x) )/3. - _G. C. Greubel_, Jan 14 2020
%p seq( ((6*n+1)*4^n -1)/3, n=0..40); # _G. C. Greubel_, Jan 14 2020
%t LinearRecurrence[{9,-24,16}, {0,9,69}, 40] (* _G. C. Greubel_, Jan 14 2020 *)
%o (PARI) a(n)=((6*n+1)*4^n-1)/3 \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Magma) [((6*n+1)*4^n -1)/3: n in [0..40]]; // _G. C. Greubel_, Jan 14 2020
%o (Sage) [((6*n+1)*4^n -1)/3 for n in (0..40)] # _G. C. Greubel_, Jan 14 2020
%o (GAP) List([0..40], n-> ((6*n+1)*4^n -1)/3); # _G. C. Greubel_, Jan 14 2020
%Y Cf. A072257, A072259, A072260.
%K nonn,easy
%O 0,2
%A N. Rathankar (rathankar(AT)yahoo.com), Jul 08 2002
%E Edited and extended by _Henry Bottomley_, Aug 06 2002
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