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A026549 Ratios of successive terms are 2,3,2,3,2,3,2,3... 7
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 (list; graph; refs; listen; history; text; internal format)
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

P. Barry, Embedding structures associated with Riordan arrays and moment matrices, 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.

G.f.: (1+2x)/(1-6x^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]

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

CROSSREFS

For n>0, a(n) = 2*A026532(n). Cf. A026551, A026567.

Cf. A010693, A208131, A109827.

Sequence in context: A099576 A303479 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

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Last modified September 21 00:17 EDT 2019. Contains 327252 sequences. (Running on oeis4.)