A036999 Restricted permutations.
6, 9, 12, 18, 27, 42, 66, 105, 168, 270, 435, 702, 1134, 1833, 2964, 4794, 7755, 12546, 20298, 32841, 53136, 85974, 139107, 225078, 364182, 589257, 953436, 1542690, 2496123, 4038810, 6534930, 10573737, 17108664, 27682398, 44791059
Offset: 0
Keywords
References
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- N. S. Mendelsohn, Permutations with confined displacement, Canad. Math. Bull., 4 (1961), 29-38.
- Index entries for linear recurrences with constant coefficients, signature (2, 0, -1).
Crossrefs
Equals A022086(n+3) + 3.
Programs
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Magma
[6] cat [3*Fibonacci(n+3)+3: n in [0..40]]; // Vincenzo Librandi, Jul 01 2017
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Mathematica
Join[{6}, Table[3 Fibonacci[n+3] + 3, {n, 0, 40}]] (* or *) CoefficientList[Series[3 (2 - x - 2 x^2) / ((x^2 + x - 1) (x - 1)), {x, 0, 33}], x] (* Vincenzo Librandi, Jul 01 2017 *)
Formula
3*A000381.
G.f.: 3*(2-x-2*x^2)/((x^2+x-1)*(x-1)). - Vincenzo Librandi, Jul 01 2017