A055389 a(0) = 1, then twice the Fibonacci sequence.

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

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

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

Essentially the same as A006355.

Cf. A000045.

Sequence in context: A262258 A293633 A006355 * A163733 A198834 A270925

Adjacent sequences: A055386 A055387 A055388 * A055390 A055391 A055392

Keyword

easy,nonn

Author

Robert G. Wilson v, Jul 05 2000

Extensions

More terms from James A. Sellers, Jul 07 2000

Status

approved