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
For n >= 2, a(n) is the least k > a(n-1) such that both k and a(n-2) + a(n-1) + k have exactly n prime factors, counted with multiplicity. - Robert Israel, Aug 06 2024
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).
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
MAPLE
seq(seq(2^i*3^j, i=j..j+1), j=0..30); # Robert Israel, Aug 06 2024
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
New definition from Ralf Stephan, Dec 01 2004
STATUS
approved