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A130823
Each odd number appears thrice.
9
1, 1, 1, 3, 3, 3, 5, 5, 5, 7, 7, 7, 9, 9, 9, 11, 11, 11, 13, 13, 13, 15, 15, 15, 17, 17, 17, 19, 19, 19, 21, 21, 21, 23, 23, 23, 25, 25, 25, 27, 27, 27, 29, 29, 29, 31, 31, 31, 33, 33, 33, 35, 35, 35, 37, 37, 37, 39, 39, 39, 41, 41, 41, 43, 43, 43, 45, 45, 45, 47, 47, 47, 49, 49
OFFSET
1,4
COMMENTS
Partial sums of 1,0,0,2,0,0,2,0,0,2,0,0,... . - Emeric Deutsch, Jul 23 2007
FORMULA
a(n) = floor((n+2)/3). - Joerg Arndt, Jan 02 2024
G.f.: x*(1 + x^3)/((1 - x)*(1 - x^3)). - Emeric Deutsch, Jul 23 2007
From Michael Somos, Aug 16 2007: (Start)
Euler transform of length 6 sequence [1, 0, 2, 0, 0, -1].
a(n + 3) = a(n) + 2.
a(n) = - a(1-n) for all n in Z. (End)
a(n) = floor((n-1)*(n+1)/3) - floor((n-2)*n/3). - Bruno Berselli, Mar 03 2017
a(n) = (6*n-3-4*sqrt(3)*sin(2*(n-2)*Pi/3))/9. - Wesley Ivan Hurt, Sep 30 2017
EXAMPLE
G.f. = x + x^2 + x^3 + 3*x^4 + 3*x^5 + 3*x^6 + 5*x^7 + 5*x^8 + 5*x^9 + 7*x^10 + ...
MAPLE
G:=x*(1+x^3)/((1-x)*(1-x^3)): Gser:=series(G, x=0, 82): seq(coeff(Gser, x, n), n= 1..75); # Emeric Deutsch, Jul 23 2007
MATHEMATICA
Flatten[Table[n, {n, 1, 49, 2}, {3}]] (* or *) LinearRecurrence[{1, 0, 1, -1}, {1, 1, 1, 3}, 100] (* or *) Accumulate[PadRight[{1}, 100, {2, 0, 0}]] (* Harvey P. Dale, Apr 20 2015 *)
PROG
(PARI) {a(n) = (n-1)\3*2+1}; \\ Michael Somos, Aug 16 2007
(Magma) [Floor((n-1)/3)*2+1: n in [1..80]]; // Vincenzo Librandi, Aug 10 2011
CROSSREFS
Sequence in context: A200266 A101290 A080605 * A101435 A373013 A077886
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Jul 17 2007
EXTENSIONS
More terms from Emeric Deutsch, Jul 23 2007
STATUS
approved