This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS 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(n-1). 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)/((1-x)^2*(x^2+x+1)). a(n)=(2*n-2-A057078(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*n-1)/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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 19:31 EST 2019. Contains 329809 sequences. (Running on oeis4.)