OFFSET
0,2
COMMENTS
a(n) is the number of sequences over the alphabet {0,1} such that all maximal blocks (of both 0's and 1's) have odd length. E.g., a(4) = 6 because we have 0001, 0101, 0111, 1000, 1010, 1110. - Geoffrey Critzer, Mar 06 2012
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..4785
Hung Viet Chu and Zachary Louis Vasseur, Weighted Schreier-type Sets and the Fibonacci Sequence, arXiv:2405.19352 [math.CO], 2024. See p. 2.
Yuhong Guo, Some Identities for Palindromic Compositions Without 2's, Journal of Mathematical Research with Applications 38.2 (2018): 130-136.
Yu-hong Guo, Some Identities for Palindromic Compositions, J. Int. Seq., Vol. 21 (2018), Article 18.6.6.
Augustine O. Munagi, Integer Compositions and Higher-Order Conjugation, J. Int. Seq., Vol. 21 (2018), Article 18.8.5.
Index entries for linear recurrences with constant coefficients, signature (1,1).
FORMULA
G.f.: (1 + x - x^2)/(1 - x - x^2).
E.g.f.: 1 + 4*exp(x/2)*sinh(sqrt(5)*x/2)/sqrt(5). - Stefano Spezia, Apr 18 2022
MATHEMATICA
Join[{1}, Table[2*Fibonacci[n], {n, 70}]] (* Vladimir Joseph Stephan Orlovsky, Feb 10 2012 *)
CoefficientList[Series[(1 + x - x^2)/(1 - x - x^2), {x, 0, 38}], x] (* Michael De Vlieger, Jun 14 2018 *)
PROG
(PARI) a(n)=if(n, 2*fibonacci(n), 1) \\ Charles R Greathouse IV, Oct 03 2016
(Magma) [1] cat [2*Fibonacci(n): n in [1..40]]; // G. C. Greubel, Apr 28 2021
(Sage) [1]+[2*fibonacci(n) for n in (1..40)] # G. C. Greubel, Apr 28 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Robert G. Wilson v, Jul 05 2000
EXTENSIONS
More terms from James A. Sellers, Jul 07 2000
STATUS
approved