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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Partial sums of 1,0,0,2,0,0,2,0,0,2,0,0,... . - Emeric Deutsch, Jul 23 2007

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, -1).

FORMULA

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) = -1 + Sum_{k=1..n} ((2/9)*((k mod 3)+4*((k+1) mod 3)-2*((k+2) mod 3))). - Paolo P. Lava, Aug 29 2007, Aug 22 2009

a(n) = floor((n-1)/3)*2 + 1. Michael Somos' formula suggested by Johannes W. Meijer. - Paolo P. Lava, Aug 21 2009

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 A077886 A096015

Adjacent sequences:  A130820 A130821 A130822 * A130824 A130825 A130826

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jul 17 2007

EXTENSIONS

More terms from Emeric Deutsch, Jul 23 2007

STATUS

approved

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Last modified May 13 02:36 EDT 2021. Contains 343836 sequences. (Running on oeis4.)