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%I #21 Dec 26 2024 15:20:30
%S 1,2,3,5,5,8,7,11,9,14,11,17,13,20,15,23,17,26,19,29,21,32,23,35,25,
%T 38,27,41,29,44,31,47,33,50,35,53,37,56,39,59,41,62,43,65,45,68,47,71,
%U 49,74,51,77,53,80,55,83,57,86,59,89,61,92,63,95,65,98,67,101,69,104,71
%N Odd numbers interlaced with numbers 3m+2.
%C The reference gives the sequence without the initial 1 and then it is "alternate 3n+2 and 2n+3".
%C An alternative solution for this sequence is to consider the first second differences repeat giving 2, 3, 5, 5, 8, 7, 11, 12, 14, 14, 17, 16, 20, 21. - Lorraine Gregory, Ed.D. (lgregory(AT)lssu.edu), Jan 19 2009
%D D. Dolan, J. Williamson and M. Muri, Mathematics Activities for Elementary School Teachers: A Problem Solving Approach, Addison Wesley Longman, Inc., NY, Fourth Edition (ISBN 0-201-61321-2), Chapter 1, Activity 2, #9.
%H Harry J. Smith, <a href="/A063914/b063914.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F From _Colin Barker_, Mar 28 2012: (Start)
%F a(n) = 2*a(n-2)-a(n-4).
%F G.f.: x*(1+2*x+x^2+x^3)/((1-x)^2*(1+x)^2). (End)
%F a(n) = (5*n - 2 + (-1)^n*(n - 2))/4. - _Andrew Howroyd_, Dec 26 2024
%p for n from 0 to 80 do printf(`%d,%d,`, 2*n+1, 3*n+2) od:
%t nn=50;Riffle[Range[1,2*nn,2],3*Range[0,nn]+2] (* _Harvey P. Dale_, Jan 16 2013 *)
%o (PARI) a(n) = { if (n%2, n, 3*n/2 - 1) } \\ _Harry J. Smith_, Sep 02 2009
%K nonn,easy,changed
%O 1,2
%A Nancy Shaffer (nancys(AT)rose.net), Aug 30 2001
%E Better description from _Brian Galebach_, Sep 05, 2001
%E More terms from _James A. Sellers_, Sep 25 2001