A154920 - OEIS

%I #23 Feb 26 2022 04:24:57

%S 1,18,27,324,405,4374,5103,52488,59049,590490,649539,6377292,6908733,

%T 66961566,71744535,688747536,731794257,6973568802,7360989291,

%U 69735688020,73222472421,690383311398,721764371007,6778308875544

%N Denominators of a ternary BBP-type formula for log(3).

%C log(3) = Sum_{k>=0} (9/(2k+1)+1/(2k+2))/9^(k+1).

%C log(3) = 1 + Sum_{k>=0} (1/(2k+2)+1/(2k+3))/9^(k+1).

%H David H. Bailey, <a href="https://www.davidhbailey.com/dhbpapers/bbp-formulas.pdf">A Compendium of BBP-Type Formulas for Mathematical Constants</a>, 2017, page 14. [From _Jaume Oliver Lafont_, Sep 25 2009]

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,18,0,-81).

%F a(n) = (n+1)*9^[(n+1)/2] = 18*a(n-2) - 81*a(n-4).

%F Sum_{n>=0} 1/a(n) = log(3).

%F G.f.: (1+18*x+9*x^2)/(1-9*x^2)^2. - _Jaume Oliver Lafont_, Jan 29 2009

%F a(n) = (2-(-1)^n)*(n+1)*3^n. - _Jaume Oliver Lafont_, Sep 27 2009

%F Sum_{n>=0} (-1)^n/a(n) = log(8/3). - _Amiram Eldar_, Feb 26 2022

%t LinearRecurrence[{0,18,0,-81},{1,18,27,324},30] (* _Harvey P. Dale_, Jan 10 2017 *)

%o (PARI) a(n)=(n+1)*9^((n+1)\2) \\ _Jaume Oliver Lafont_, Mar 25 2009

%o (Magma) [(2-(-1)^n)*(n+1)*3^n: n in [0..30]]; // _Vincenzo Librandi_, Jul 06 2015

%Y Cf. A002391, A058962.

%Y Cf. A164985, A165132. - _Jaume Oliver Lafont_, Sep 25 2009

%K nonn

%O 0,2

%A _Jaume Oliver Lafont_, Jan 17 2009, Jan 18 2009