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
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).
Programs
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Magma
[1] cat [2*Fibonacci(n): n in [1..40]]; // G. C. Greubel, Apr 28 2021
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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 *) -
PARI
a(n)=if(n,2*fibonacci(n),1) \\ Charles R Greathouse IV, Oct 03 2016
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Sage
[1]+[2*fibonacci(n) for n in (1..40)] # G. C. Greubel, Apr 28 2021
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
Extensions
More terms from James Sellers, Jul 07 2000
Comments