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A131534 Period 3: repeat [1, 2, 1]. 23
1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A106510. Inverse binomial transform of A024495 (without leading zeros). - Philippe Deléham, Nov 26 2008

a(n) = A130196(n) - A022003(n) = A080425(n) - A130196(n)+2 = A153727(n)/A130196(n). - Reinhard Zumkeller, Nov 12 2009

Continued fraction expansion of A177346, (1+sqrt(10))/3. - Klaus Brockhaus, May 07 2010

a(n) = GCD of terms of the sequence S_n = {F_i+F_{i+1}+F_{i+2}+...+F_{i+2n}, i >= 0}, where F_i denotes a Fibonacci number. (See A210209.) - Daniel Forgues, May 04 2016

a(n) = GCD of terms of the sequence S_n = {L_i+L_{i+1}+L_{i+2}+...+L_{i+2n}, i >= 0}, where L_i denotes a Lucas number. (See A229339.) - Daniel Forgues, May 04 2016

LINKS

Table of n, a(n) for n=0..104.

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

FORMULA

a(n) = (1/9)*(4*(n mod 3)+7*((n+1) mod 3)+((n+2) mod 3)). - Paolo P. Lava, Aug 28 2007

G.f.: (x+1)^2/((1-x)*(x^2+x+1)). - R. J. Mathar, Nov 14 2007

a(n) = 4/3+(2/3)*cos(2*Pi*(n+2)/3). - Jaume Oliver Lafont, May 09 2008

a(n) = A101825(n+1). - R. J. Mathar, Jun 13 2008

a(n) = 4/3+1/3*(-1/2-(1/2*I)*sqrt(3))^(-2)*(-1/2-(1/2*I)*sqrt(3))^n+1/3*(-1/2+(1/2*I) *sqrt(3))^(-2)*(-1/2+(1/2*I)*sqrt(3))^n+1/3*(-1/2-(1/2*I)*sqrt(3))^n+1/3*(-1/2 +(1/2*I)*sqrt(3))^n+2/3*(-1/2-(1/2*I)*sqrt(3))^(-1)*(-1/2-(1/2*I)*sqrt(3))^n+2/3 *(-1/2+(1/2*I)*sqrt(3))^(-1)*(-1/2+(1/2*I)*sqrt(3))^n, with I=sqrt(-1). - Paolo P. Lava, Nov 27 2008

a(n) = gcd(F(n)^2+F(n+1)^2, F(n)+F(n+1)). - Gary Detlefs, Dec 29 2010

a(n) = 2-((n+2)^2 mod 3). - Gary Detlefs, Oct 13 2011

a(n) = ceiling(n*4/3) - ceiling((n-1)*4/3). - Tom Edgar, Jul 22 2014

a(n) = 2-abs(3*floor(n/3)+1-n). - Mikael Aaltonen, Jan 02 2015

a(n) = 1+[3|(2n+1)], using Iverson bracket. - Daniel Forgues, May 04 2016

a(n) = a(n-3) for n>2. - Wesley Ivan Hurt, Jul 05 2016

MAPLE

A131534:=n->(-n mod 3)^(n mod 3): seq(A131534(n), n=0..100); # Wesley Ivan Hurt, Aug 29 2014

MATHEMATICA

PadRight[{}, 120, {1, 2, 1}] (* Harvey P. Dale, Aug 06 2013 *)

PROG

(PARI) a(n)=1+(n%3==1) \\ Jaume Oliver Lafont, Mar 20 2009

(MAGMA) [(-n mod 3)^(n mod 3) : n in [0..100]]; // Wesley Ivan Hurt, Aug 29 2014

CROSSREFS

Cf. A167808. - Reinhard Zumkeller, Nov 12 2009

Cf. A000045, A022003, A024495, A080425, A101825, A106510, A130196, A153727, A177346, A210209, A229339.

Sequence in context: A087204 A101825 A177702 * A061347 A115579 A115573

Adjacent sequences:  A131531 A131532 A131533 * A131535 A131536 A131537

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Aug 26 2007

STATUS

approved

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Last modified July 20 16:34 EDT 2019. Contains 325185 sequences. (Running on oeis4.)