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A055389 a(0) = 1, then twice the Fibonacci sequence. 14
1, 2, 2, 4, 6, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634, 78176338 (list; graph; refs; listen; history; text; internal format)
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
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.
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
Essentially the same as A006355.
Cf. A000045.
Sequence in context: A262258 A293633 A006355 * A163733 A198834 A270925
KEYWORD
easy,nonn
AUTHOR
Robert G. Wilson v, Jul 05 2000
EXTENSIONS
More terms from James A. Sellers, Jul 07 2000
STATUS
approved

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Last modified February 28 05:33 EST 2024. Contains 370379 sequences. (Running on oeis4.)