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%I #53 Sep 08 2022 08:46:18
%S 0,1,2,9,10,11,18,19,20,27,28,29,36,37,38,45,46,47,54,55,56,63,64,65,
%T 72,73,74,81,82,83,90,91,92,99,100,101,108,109,110,117,118,119,126,
%U 127,128,135,136,137,144,145,146,153,154,155,162,163,164,171,172,173,180,181,182,189
%N a(n) = n + 6*floor(n/3).
%C Equivalently, numbers that are congruent to {0, 1, 2} mod 9.
%C Also numbers m such that floor(m/3) = 3*floor(m/9).
%C The n-th term is 3*n, 3*n-2 or 3*n-4.
%C For n > 0, numbers k such that 3 | floor(k/3). - _Wesley Ivan Hurt_, Dec 01 2020
%H Bruno Berselli, <a href="/A281899/b281899.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F G.f.: x*(1 + x + 7*x^2)/((1 - x)^2*(1 + x + x^2)).
%F a(n) = a(n-1) + a(n-3) - a(n-4).
%F a(n) = 3*n - 2*(n mod 3). In general, n + 3*h*floor(n/3) = (h+1)*n - h*(n mod 3).
%F a(n) + a(n+s) = a(2*n+s-1) + 1, where s is nonnegative and not divisible by 3. Example: for s=14, a(n) + a(n+14) = a(2*n+13) + 1; for n=3, a(3) + a(17) = a(19) + 1 = 9 + 47 = 55 + 1 = 56.
%F a(6*k+r) = 18*k + a(r), where 0 <= r <= 5.
%F a(n) = 7*A002264(n) + A002264(n+1) + A002264(n+2).
%p A281899:=n->n+6*floor(n/3): seq(A281899(n), n=0..100); # _Wesley Ivan Hurt_, Feb 09 2017
%t Table[n + 6 Floor[n/3], {n, 0, 70}]
%t LinearRecurrence[{1,0,1,-1},{0,1,2,9},90] (* _Harvey P. Dale_, Feb 25 2018 *)
%o (PARI) a(n)=n\3*6 + n \\ _Charles R Greathouse IV_, Feb 07 2017
%o (Python) [n+6*int(n/3) for n in range(70)]
%o (Sage) [n+6*floor(n/3) for n in range(70)]
%o (Maxima) makelist(n+6*floor(n/3), n, 0, 70);
%o (Magma) [n+6*(n div 3): n in [0..70]];
%Y Cf. A002264.
%Y Subsequence of A060464 and A248375.
%Y The first differences are in A105395.
%Y Cf. similar sequences with formula n+i*floor(n/3): A004773 (i=1), A047217 (i=2), A047240 (i=3), A047354 (i=4), A047469 (i=5), this sequence (i=6).
%Y Cf. numbers that are congruent to {0, 1, 2} mod j: the sequences are listed in the previous row for j = 4..9, respectively.
%K nonn,easy
%O 0,3
%A _Bruno Berselli_, Feb 06 2017
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