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%I #23 Oct 11 2023 15:18:28
%S 1,5,4,11,7,17,10,23,13,29,16,35,19,41,22,47,25,53,28,59,31,65,34,71,
%T 37,77,40,83,43,89,46,95,49,101,52,107,55,113,58,119,61,125,64,131,67,
%U 137,70,143,73,149,76,155,79,161,82,167,85,173,88,179,91,185,94,191,97,197
%N Trisection a(n) = A026741(3n + 2).
%C The other trisections are A165351 and A165355.
%H John M. Campbell, <a href="http://arxiv.org/abs/1105.3399">An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache Sequences</a>, arXiv preprint arXiv:1105.3399 [math.GM], 2011.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1)
%F a(n)*A022998(n) = A045944(n).
%F a(n)*A026741(n+1) = A000326(n+1).
%F a(2n) = A016777(n); a(2n+1) = A016969(n).
%F From _R. J. Mathar_ Nov 22 2009: (Start)
%F a(n) = 2*a(n-2) - a(n-4).
%F G.f.: (1 + 5*x + 2*x^2 + x^3)/((1-x)^2*(1+x)^2). (End)
%p A026741 := proc(n) if type(n,'odd') then n; else n/2 ; fi; end:
%p A165367 := proc(n) A026741(3*n+2) ; end: seq(A165367(n),n=0..100) ; # _R. J. Mathar_, Nov 22 2009
%t LinearRecurrence[{0, 2, 0, -1}, {1, 5, 4, 11}, 66] (* _Jean-François Alcover_, Nov 15 2017 *)
%o (PARI) a(n) = (3*n+2)>>!(n%2); \\ _Ruud H.G. van Tol_, Oct 09 2023
%Y Cf. A000326, A016777, A016969, A022998, A026741, A045944, A165351, A165355.
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Sep 17 2009
%E All comments rewritten as formulas by _R. J. Mathar_, Nov 22 2009
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