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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The other trisections are A165351 and A165355.

LINKS

Table of n, a(n) for n=0..65.

John M. Campbell, An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache Sequences, arXiv preprint arXiv:1105.3399, 2011.

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1)

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 *)

CROSSREFS

Sequence in context: A089520 A163524 A051552 * A166549 A232894 A262902

Adjacent sequences:  A165364 A165365 A165366 * A165368 A165369 A165370

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Sep 17 2009

EXTENSIONS

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

STATUS

approved

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Last modified October 21 12:49 EDT 2018. Contains 316421 sequences. (Running on oeis4.)