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%I #17 Aug 06 2021 16:25:18
%S 1,2,3,5,7,6,9,12,9,13,17,12,17,22,15,21,27,18,25,32,21,29,37,24,33,
%T 42,27,37,47,30,41,52,33,45,57,36,49,62,39,53,67,42,57,72,45,61,77,48,
%U 65,82,51,69,87,54,73,92,57,77,97,60,81,102,63,85,107,66,89,112,69,93,117
%N a(n) = n + A115273(n), where A115273(n) = 0 for n = 1..3.
%C Three arithmetic progressions interlaced: a(1..3) = 1..3 and d = a(n+3)-a(n) = 4,5,3.
%H Colin Barker, <a href="/A115274/b115274.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%F a(n) = n+floor(n/3)*(n mod 3), n = 1, 2, ...
%F a(n) = 2*a(n-3)-a(n-6). - _Colin Barker_, May 11 2015
%F G.f.: x*(3*x^4+3*x^3+3*x^2+2*x+1) / ((x-1)^2*(x^2+x+1)^2). - _Colin Barker_, May 11 2015
%F E.g.f.: (-5+12*x)*exp(x)/9 + (3+2*x)*sqrt(3)*exp(-x/2)*sin(sqrt(3)*x/2)/9 + 5*exp(-x/2)*cos(sqrt(3)*x/2)/9. - _Robert Israel_, May 11 2015
%p seq(op([1+4*j,2+5*j,3+3*j]),j=0..100); # _Robert Israel_, May 11 2015
%t Table[n+Floor[n/3]*Mod[n, 3], {n, 78}]
%t LinearRecurrence[{0,0,2,0,0,-1},{1,2,3,5,7,6},80] (* _Harvey P. Dale_, Aug 06 2021 *)
%o (PARI) Vec(x*(3*x^4+3*x^3+3*x^2+2*x+1) / ((x-1)^2*(x^2+x+1)^2) + O(x^100)) \\ _Colin Barker_, May 11 2015
%Y Cf. A115273.
%K nonn,easy
%O 1,2
%A _Zak Seidov_, Jan 18 2006
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