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%I #16 Sep 08 2022 08:45:06
%S 12,57,261,1173,5205,22869,99669,431445,1856853,7951701,33903957,
%T 144004437,609572181,2572506453,10826896725,45455070549,190410216789,
%U 796000605525,3321441375573,13835521316181,57541108520277,238960527103317,991026480502101
%N a(n) = ((6*n+37)*4^n - 1)/3.
%C Related to Collatz function (for n>0). All terms are divisible by 3.
%H G. C. Greubel, <a href="/A072259/b072259.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*(4-17*x+12*x^2)/((1-x)*(1-4*x)^2). - Bruno Berselli, Dec 16 2011
%F E.g.f.: ((37 + 24*x)*exp(4*x) - exp(x))/3. - _G. C. Greubel_, Jan 14 2020
%p seq( ((6*n+37)*4^n -1)/3, n=0..30); # _G. C. Greubel_, Jan 14 2020
%t LinearRecurrence[{9,-24,16},{12,57,261},30] (* _Harvey P. Dale_, Mar 10 2018 *)
%o (PARI) a(n)=((6*n+37)*4^n-1)/3 \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Magma) [((6*n+37)*4^n -1)/3: n in [0..30]]; // _G. C. Greubel_, Jan 14 2020
%o (Sage) [((6*n+37)*4^n -1)/3 for n in (0..30)] # _G. C. Greubel_, Jan 14 2020
%o (GAP) List([0..30], n-> ((6*n+37)*4^n -1)/3); # _G. C. Greubel_, Jan 14 2020
%Y Cf. A072257, A072258, A072260.
%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
%E More terms from _Harvey P. Dale_, Mar 10 2018
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