A165367 Trisection a(n) = A026741(3n + 2).

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

Author

Paul Curtz, Sep 17 2009

Keywords

• nonn
• easy

Comments

The other trisections are A165351 and A165355.

Links

• John M. Campbell, An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache Sequences, arXiv preprint arXiv:1105.3399 [math.GM], 2011.
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1)

Crossrefs

Cf. A000326, A016777, A016969, A022998, A026741, A045944, A165351, A165355.

Programs

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 *)

PARI

a(n) = (3*n+2)>>!(n%2); \\ Ruud H.G. van Tol, Oct 09 2023

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)

Extensions

All comments rewritten as formulas by R. J. Mathar, Nov 22 2009