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A265228 Interleave the even numbers with the numbers that are congruent to {1, 3, 7} mod 8.

%I A265228 #49 Dec 13 2015 08:58:04
%S A265228 0,1,2,3,4,7,6,9,8,11,10,15,12,17,14,19,16,23,18,25,20,27,22,31,24,33,
%T A265228 26,35,28,39,30,41,32,43,34,47,36,49,38,51,40,55,42,57,44,59,46,63,48,
%U A265228 65,50,67,52,71,54,73,56,75,58,79,60,81,62,83,64,87,66
%N A265228 Interleave the even numbers with the numbers that are congruent to {1, 3, 7} mod 8.
%C A265228 b(n) denotes the sequence:
%C A265228 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, 1, 2, -2, 2, -2, 2, -2, 2, 3, -3, 3, -3, 3, -3, 3, 4, -4, ..., and
%C A265228 c(n) = n + b(n) = n + floor((n+1)/7)*(-1)^((n+1) mod 7) provides:
%C A265228 0, 1, 2, 3, 4, 5, 7, 6, 9, 8, 11, 10, 13, 15, 12, 17, 14, 19, 16, 21, 23, 18, 25, 20, 27, 22, 29, ..., which is a permutation of A001477.
%C A265228 a(n) differs from c(n) because c(n) contains the terms of the form 8*k+5.
%H A265228 Colin Barker, <a href="/A265228/b265228.txt">Table of n, a(n) for n = 0..1000</a>
%H A265228 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,1,0,-1).
%F A265228 a(n) = n + 2*A260160(n) = n + (1-(-1)^n)*floor(n/6+1/3). Therefore, for odd n, a(n) = A047529((n+1)/2); otherwise, a(n) = n.
%F A265228 a(n) = a(n-6) - (-1)^n + 7.
%F A265228 a(n) = A260708(n) - A260699(n-1) - A079979(n+3), with A260699(-1) = 0.
%F A265228 From _Colin Barker_, Dec 06 2015: (Start)
%F A265228 a(n) = a(n-2) + a(n-6) - a(n-8) for n > 7.
%F A265228 G.f.: x*(1+2*x+2*x^2+2*x^3+4*x^4+2*x^5+x^6) / ((1-x)^2*(1+x)^2*(1-x+x^2)*(1+x+x^2)). (End)
%t A265228 lim = 11; Riffle[Range[0, 6 lim, 2], Select[Range[8 lim], MemberQ[{1, 3, 7}, Mod[#, 8]] &]] (* _Michael De Vlieger_, Dec 06 2015 *)
%o A265228 (PARI) concat(0, Vec(x*(1+2*x+2*x^2+2*x^3+4*x^4+2*x^5+x^6)/((1-x)^2 *(1+x)^2*(1-x+x^2)*(1+x+x^2)) + O(x^100))) \\ _Colin Barker_, Dec 06 2015
%o A265228 (PARI) vector(100, n, n--; n+(1-(-1)^n)*floor(n/6+1/3)) \\ _Altug Alkan_, Dec 09 2015
%Y A265228 Cf. A001477, A004770, A005843, A047529, A079979, A260160, A260699, A260708.
%K A265228 nonn,easy
%O A265228 0,3
%A A265228 _Paul Curtz_, Dec 06 2015