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URL: https://oeis.org/A165367

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A165367
Trisection a(n) = A026741(3n + 2).
7
1, 5, 4, 11, 7, 17, 10, 23, 13, 29, 16, 35, 19, 41, 22, 47, 25, 53, 28, 59, 31, 65, 34, 71, 37, 77, 40, 83, 43, 89, 46, 95, 49, 101, 52, 107, 55, 113, 58, 119, 61, 125, 64, 131, 67, 137, 70, 143, 73, 149, 76, 155, 79, 161, 82, 167, 85, 173, 88, 179, 91, 185, 94, 191, 97, 197
OFFSET
0,2
COMMENTS
The other trisections are A165351 and A165355.
FORMULA
a(n)*A022998(n) = A045944(n).
a(n)*A026741(n+1) = A000326(n+1).
a(2n) = A016777(n); a(2n+1) = A016969(n).
From R. J. Mathar Nov 22 2009: (Start)
a(n) = 2*a(n-2) - a(n-4).
G.f.: (1 + 5*x + 2*x^2 + x^3)/((1-x)^2*(1+x)^2). (End)
MAPLE
A026741 := proc(n) if type(n, 'odd') then n; else n/2 ; fi; end:
A165367 := proc(n) A026741(3*n+2) ; end: seq(A165367(n), n=0..100) ; # R. J. Mathar, Nov 22 2009
MATHEMATICA
LinearRecurrence[{0, 2, 0, -1}, {1, 5, 4, 11}, 66] (* Jean-François Alcover, Nov 15 2017 *)
PROG
(PARI) a(n) = (3*n+2)>>!(n%2); \\ Ruud H.G. van Tol, Oct 09 2023
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Sep 17 2009
EXTENSIONS
All comments rewritten as formulas by R. J. Mathar, Nov 22 2009
STATUS
approved