A026549 Ratios of successive terms are 2, 3, 2, 3, 2, 3, 2, 3, ...

1, 2, 6, 12, 36, 72, 216, 432, 1296, 2592, 7776, 15552, 46656, 93312, 279936, 559872, 1679616, 3359232, 10077696, 20155392, 60466176, 120932352, 362797056, 725594112, 2176782336, 4353564672, 13060694016, 26121388032, 78364164096, 156728328192, 470184984576, 940369969152

Offset

0,2

Comments

Appears to be the number of permutations p of {1,2,...,n} such that p(i)+p(i+1)>=n for every i=1,2,...,n-1 (if offset is 1). - Vladeta Jovovic, Dec 15 2003

Equals eigensequence of a triangle with 1's in even columns and (1,3,3,3,...) in odd columns. a(5) = 72 = (1, 3, 1, 3, 1, 1) dot (1, 1, 2, 6, 12, 36) = (1 + 3 + 2 + 18 + 12 + 36), where (1, 3, 1, 3, 1, 1) = row 5 of the generating triangle. - Gary W. Adamson, Aug 02 2010

Partial products of A010693. - Reinhard Zumkeller, Mar 29 2012

Satisfies Benford's law [Theodore P. Hill, Personal communication, Feb 06, 2017]. - N. J. A. Sloane, Feb 08 2017

References

Arno Berger and Theodore P. Hill, An Introduction to Benford's Law, Princeton University Press, 2015.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..700

Paul Barry, Embedding structures associated with Riordan arrays and moment matrices, International Journal of Combinatorics, Vol. 2014 (2014), Article ID 301394, 7 pages; arXiv preprint, arXiv:1312.0583 [math.CO], 2013.

Index entries for linear recurrences with constant coefficients, signature (0,6).

Index entries for sequences related to Benford's law.

Formula

Equals T(n, 0) + T(n, 1) + ... + T(n, 2n), T given by A026536.

a(n) = 2*A026532(n), for n > 0.

G.f.: (1+2*x)/(1-6*x^2) - Paul Barry, Aug 25 2003

a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011

a(n) = (1/2)*(3 - (-1)^n)*6^floor(n/2), or a(n) = 6*a(n-2). - Vincenzo Librandi, Jun 08 2011

a(n) = 1/a(-n) if n is even and (2/3)/a(-n) if n is odd for all n in Z. - Michael Somos, Apr 09 2022

Sum_{n>=0} 1/a(n) = 9/5. - Amiram Eldar, Feb 13 2023

Example

G.f. = 1 + 2*x + 6*x^2 + 12*x^3 + 36*x^4 + 72*x^5 + 216*x^6 + ... - Michael Somos, Apr 09 2022

Mathematica

LinearRecurrence[{0, 6}, {1, 2}, 30] (* Harvey P. Dale, May 29 2016 *)

Prog

(Magma) [(1/2)*(3-(-1)^n)*6^Floor(n/2): n in [0..30]]; // Vincenzo Librandi, Jun 08 2011
(Haskell)
a026549 n = a026549_list !! n
a026549_list = scanl (*) 1 $ a010693_list
-- Reinhard Zumkeller, Mar 29 2012
(SageMath) [(1+(n%2))*6^(n//2) for n in (0..30)] # G. C. Greubel, Apr 09 2022
(PARI) {a(n) = 6^(n\2) * (n%2+1)}; /* Michael Somos, Apr 09 2022 */

Crossrefs

Cf. A026532, A026536, A026551, A026567.

Cf. A010693, A208131, A109827.

Sequence in context: A303479 A347452 A307015 * A120766 A121404 A202337

Adjacent sequences: A026546 A026547 A026548 * A026550 A026551 A026552

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

New definition from Ralf Stephan, Dec 01 2004

Status

approved