The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A124647 a(n) = (2n + 1)*3^n. 5
 1, 9, 45, 189, 729, 2673, 9477, 32805, 111537, 373977, 1240029, 4074381, 13286025, 43046721, 138706101, 444816117, 1420541793, 4519905705, 14334558093, 45328197213, 142958160441, 449795187729, 1412147682405, 4424729404869 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 1 - 1/9 + 1/45 - 1/189 + ... = Pi/(2*sqrt(3)) = A093766. [Jolley eq 271]. If X_1,X_2,...,X_n are 3-blocks of a (4n+1)-set X then, for n>=1, a(n) is the number of (n+1)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan Janjic, Nov 23 2007 Sum_{k>=0} 1/a(k) = log(2+sqrt(3))*sqrt(3)/2 =  1.1405189944... - Jaume Oliver Lafont, Nov 30 2009 REFERENCES L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 50 LINKS Milan Janjic, Two Enumerative Functions Index entries for linear recurrences with constant coefficients, signature (6,-9). FORMULA G.f.: (1+3*x)/(1-3*x)^2. - Jaume Oliver Lafont, Mar 07 2009 a(n) = 6*a(n-1) - 9*a(n-2) for n > 1; a(0) = 1, a(1) = 9. - Klaus Brockhaus, Sep 23 2009 a(n) = 9*A081038(n-1) for n > 0. - Klaus Brockhaus, Sep 23 2009 a(n) = Sum_{i=1..2*3^n-1} gcd(i,2*3^n) = A018804(2*3^n) -2*3^n. This is an application of the multiplicative property of the gcd sum-function A018804. So we get: 2*3^0 * phi(3^n) + ... + 2*3^(n-1) * phi(3^1) + 2*3^n * phi(3^0)+3^0 * phi(2*3^n) + ... + 3^n * phi(2*3^0) - gcd(2*3^n,2*3^n) = a(n), where phi=A000010 is Euler's totient. A general formula is Sum_{i=1..2*p^n-1} gcd(i,2*p^n) = n*3*p^n * n - 3*n*p^(n-1) + p^n, for p an odd prime. This sequence correspondes to p=3. - Jeffrey R. Goodwin, Nov 10 2011 EXAMPLE a(3) = 189 = 7*(3^3). PROG (MAGMA) [ (2*n+1)*3^n: n in [0..23] ]; // Klaus Brockhaus, Sep 23 2009 CROSSREFS Sequence in context: A022574 A321948 A050574 * A111640 A024209 A179855 Adjacent sequences:  A124644 A124645 A124646 * A124648 A124649 A124650 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Dec 22 2006 EXTENSIONS More terms from Klaus Brockhaus, Sep 23 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 20 20:26 EDT 2021. Contains 343137 sequences. (Running on oeis4.)