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%I #68 Feb 13 2023 02:53:54
%S 1,2,6,12,36,72,216,432,1296,2592,7776,15552,46656,93312,279936,
%T 559872,1679616,3359232,10077696,20155392,60466176,120932352,
%U 362797056,725594112,2176782336,4353564672,13060694016,26121388032,78364164096,156728328192,470184984576,940369969152
%N Ratios of successive terms are 2, 3, 2, 3, 2, 3, 2, 3, ...
%C 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
%C 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
%C Partial products of A010693. - _Reinhard Zumkeller_, Mar 29 2012
%C Satisfies Benford's law [Theodore P. Hill, Personal communication, Feb 06, 2017]. - _N. J. A. Sloane_, Feb 08 2017
%D Arno Berger and Theodore P. Hill, An Introduction to Benford's Law, Princeton University Press, 2015.
%H Vincenzo Librandi, <a href="/A026549/b026549.txt">Table of n, a(n) for n = 0..700</a>
%H Paul Barry, <a href="http://dx.doi.org/10.1155/2014/301394">Embedding structures associated with Riordan arrays and moment matrices</a>, International Journal of Combinatorics, Vol. 2014 (2014), Article ID 301394, 7 pages; <a href="http://arxiv.org/abs/1312.0583">arXiv preprint</a>, arXiv:1312.0583 [math.CO], 2013.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,6).
%H <a href="/index/Be#Benford">Index entries for sequences related to Benford's law</a>.
%F Equals T(n, 0) + T(n, 1) + ... + T(n, 2n), T given by A026536.
%F a(n) = 2*A026532(n), for n > 0.
%F G.f.: (1+2*x)/(1-6*x^2) - _Paul Barry_, Aug 25 2003
%F a(n+3) = a(n+2)*a(n+1)/a(n). - _Reinhard Zumkeller_, Mar 04 2011
%F a(n) = (1/2)*(3 - (-1)^n)*6^floor(n/2), or a(n) = 6*a(n-2). - _Vincenzo Librandi_, Jun 08 2011
%F 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
%F Sum_{n>=0} 1/a(n) = 9/5. - _Amiram Eldar_, Feb 13 2023
%e 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
%t LinearRecurrence[{0,6},{1,2},30] (* _Harvey P. Dale_, May 29 2016 *)
%o (Magma) [(1/2)*(3-(-1)^n)*6^Floor(n/2): n in [0..30]]; // _Vincenzo Librandi_, Jun 08 2011
%o (Haskell)
%o a026549 n = a026549_list !! n
%o a026549_list = scanl (*) 1 $ a010693_list
%o -- _Reinhard Zumkeller_, Mar 29 2012
%o (SageMath) [(1+(n%2))*6^(n//2) for n in (0..30)] # _G. C. Greubel_, Apr 09 2022
%o (PARI) {a(n) = 6^(n\2) * (n%2+1)}; /* _Michael Somos_, Apr 09 2022 */
%Y Cf. A026532, A026536, A026551, A026567.
%Y Cf. A010693, A208131, A109827.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_
%E New definition from _Ralf Stephan_, Dec 01 2004
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