

A131737


Essentially even numbers followed by duplicated odd numbers.


2



0, 1, 1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 43, 43, 44, 45
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OFFSET

0,5


LINKS

Table of n, a(n) for n=0..68.
Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, 1).


FORMULA

a(0)=0. a(1)=a(2)=1. a(3*n)=A005408(n1). a(3*n+1)=a(3*n)+1. a(3*n+2)=a(3*n)+2, n>0.
O.g.f.: x*(1+x^4)/((1x)^2*(x^2+x+1)). a(n)=(2*n2A057078(n))/3, n>1.  R. J. Mathar, Jul 16 2008
a(n) = (1/9)*Sum{k=0..n}{5*(k mod 3)+2*((k+1) mod 3)((k+2) mod 3)}1+(C(2*n,n) mod 2)+{C((n+1)^2,n+3) mod 2}, with n>=0.  Paolo P. Lava, Oct 07 2008 (corrected by Johannes W. Meijer, Jun 27 2011)
Euler transform of length 8 sequence [ 1, 0, 1, 1, 0, 0, 0, 1].  Michael Somos, Jan 11 2011
0 = a(n)  a(n+1)  a(n+3) + a(n+4) if n>1.  Michael Somos, Nov 11 2015
a(n) = floor((2*n1)/3) for n > 1.  Werner Schulte, Feb 27 2019


EXAMPLE

G.f. = x + x^2 + x^3 + 2*x^4 + 3*x^5 + 3*x^6 + 4*x^7 + 5*x^8 + 5*x^9 + 6*x^10 + ...


MAPLE

A131737 := proc(n): (1/9)*add(5*(k mod 3)+2*((k+1) mod 3)((k+2) mod 3), k=0..n)1+(binomial(2*n, n) mod 2)+(binomial((n+1)^2, n+3) mod 2) end: seq( A131737(n), n=0..74); # Johannes W. Meijer, Jun 27 2011


MATHEMATICA

Join[{0, 1}, LinearRecurrence[{1, 0, 1, 1}, {1, 1, 2, 3}, 68]] (* Georg Fischer, Feb 27 2019 *)


PROG

(PARI) {a(n) = (n==0) + (n==1) + (n\3)*2 + (n%3)  1}; /* Michael Somos, Jan 11 2011 */


CROSSREFS

Cf. A004396.
Sequence in context: A317686 A156689 A168052 * A004396 A066481 A248103
Adjacent sequences: A131734 A131735 A131736 * A131738 A131739 A131740


KEYWORD

nonn,easy,less


AUTHOR

Paul Curtz, Sep 19 2007


EXTENSIONS

Edited by R. J. Mathar, Jul 16 2008


STATUS

approved



