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A281899
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a(n) = n + 6*floor(n/3).
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7
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0, 1, 2, 9, 10, 11, 18, 19, 20, 27, 28, 29, 36, 37, 38, 45, 46, 47, 54, 55, 56, 63, 64, 65, 72, 73, 74, 81, 82, 83, 90, 91, 92, 99, 100, 101, 108, 109, 110, 117, 118, 119, 126, 127, 128, 135, 136, 137, 144, 145, 146, 153, 154, 155, 162, 163, 164, 171, 172, 173, 180, 181, 182, 189
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OFFSET
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0,3
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COMMENTS
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Equivalently, numbers that are congruent to {0, 1, 2} mod 9.
Also numbers m such that floor(m/3) = 3*floor(m/9).
The n-th term is 3*n, 3*n-2 or 3*n-4.
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LINKS
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FORMULA
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G.f.: x*(1 + x + 7*x^2)/((1 - x)^2*(1 + x + x^2)).
a(n) = a(n-1) + a(n-3) - a(n-4).
a(n) = 3*n - 2*(n mod 3). In general, n + 3*h*floor(n/3) = (h+1)*n - h*(n mod 3).
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.
a(6*k+r) = 18*k + a(r), where 0 <= r <= 5.
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MAPLE
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MATHEMATICA
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Table[n + 6 Floor[n/3], {n, 0, 70}]
LinearRecurrence[{1, 0, 1, -1}, {0, 1, 2, 9}, 90] (* Harvey P. Dale, Feb 25 2018 *)
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PROG
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(Python) [n+6*int(n/3) for n in range(70)]
(Sage) [n+6*floor(n/3) for n in range(70)]
(Maxima) makelist(n+6*floor(n/3), n, 0, 70);
(Magma) [n+6*(n div 3): n in [0..70]];
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CROSSREFS
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The first differences are in A105395.
Cf. numbers that are congruent to {0, 1, 2} mod j: the sequences are listed in the previous row for j = 4..9, respectively.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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