Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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