login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A109613 Odd numbers repeated. 71
1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 17, 17, 19, 19, 21, 21, 23, 23, 25, 25, 27, 27, 29, 29, 31, 31, 33, 33, 35, 35, 37, 37, 39, 39, 41, 41, 43, 43, 45, 45, 47, 47, 49, 49, 51, 51, 53, 53, 55, 55, 57, 57, 59, 59, 61, 61, 63, 63, 65, 65, 67, 67, 69, 69, 71, 71, 73 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The number of rounds in a round-robin tournament with n competitors. - A. Timothy Royappa, Aug 13 2011

a(n) = A052928(n) + 1 = 2*A004526(n) + 1.

a(n) = A028242(n) + A110654(n).

Diagonal sums of number triangle A113126. - Paul Barry, Oct 14 2005

When partitioning a convex n-gon by all the diagonals, the maximum number of sides in resulting polygons is 2*floor(n/2)+1 = a(n-1) (from Moscow Olympiad problem 1950). - Tanya Khovanova, Apr 06 2008

Its ordinal transform is A000034. - Paolo P. Lava, Jun 25 2009

The inverse values of the coefficients in the series expansion of f(x) = (1/2)*(1+x)*log((1+x)/(1-x)) lead to this sequence; cf. A098557. - Johannes W. Meijer, Nov 12 2009

From Reinhard Zumkeller, Dec 05 2009: (Start)

First differences: A010673; partial sums: A000982;

A059329(n) = Sum_{k=0..n} a(k)*a(n-k);

A167875(n) = Sum_{k=0..n} a(k)*A005408(n-k);

A171218(n) = Sum_{k=0..n} a(k)*A005843(n-k);

A008794(n+2) = Sum_{k=0..n} a(k)*A059841(n-k). (End)

Dimension of the space of weight 2n+4 cusp forms for Gamma_0(5). - Michael Somos, May 29 2013

For n > 4: a(n) = A230584(n) - A230584(n-2). - Reinhard Zumkeller, Feb 10 2015

The arithmetic function v+-(n,2) as defined in A290988. - Robert Price, Aug 22 2017

For n > 0, also the chromatic number of the (n+1)-triangular (Johnson) graph. - Eric W. Weisstein, Nov 17 2017

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Chromatic Number

Eric Weisstein's World of Mathematics, Johnson Graph

Eric Weisstein's World of Mathematics, Triangular Graph

Wikipedia, Round-robin tournament

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

FORMULA

a(n) = 2*floor(n/2) + 1.

a(n) = A052938(n-2) + A084964(n-2) for n > 1. - Reinhard Zumkeller, Aug 27 2005

G.f.: (1+x+x^2+x^3)/(1-x^2)^2. - Paul Barry, Oct 14 2005

a(n) = n+(1+(-1)^n)/2. - Paolo P. Lava, May 08 2007

a(n) = 2*a(n-2) - a(n-4), a(0)=1, a(1)=1, a(2)=3, a(3)=3. - Philippe Deléham, Nov 03 2008

a(n) = A001477(n) + A059841(n). - Philippe Deléham, Mar 31 2009

a(n) = 2*n-a(n-1), with a(0)=1. - Vincenzo Librandi, Nov 13 2010

a(n) = R(n,-2), where R(n,x) is the n-th row polynomial of A211955. a(n) = (-1)^n + 2*Sum_{k = 1..n} (-1)^(n-k-2)*4^(k-1)*binomial(n+k,2*k). Cf. A084159. - Peter Bala, May 01 2012

a(n) = A182579(n+1,n). - Reinhard Zumkeller, May 06 2012

G.f.: ( 1+x^2 ) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 12 2016

E.g.f.: x*exp(x) + cosh(x). - Ilya Gutkovskiy, Jul 12 2016

From Guenther Schrack, Sep 10 2018: (Start)

a(-n) = -a(n-1).

a(n) = A047270(n+1) - (2*n + 2).

a(n) = A005408(A004526(n)). (End)

EXAMPLE

G.f. = 1 + x + 3*x^2 + 3*x^3 + 5*x^4 + 5*x^5 + 7*x^6 + 7*x^7 + 9*x^8 + 9*x^9 + ...

MAPLE

A109613:=n->2*floor(n/2)+1; seq(A109613(k), k=0..100); # Wesley Ivan Hurt, Oct 22 2013

MATHEMATICA

Flatten@ Array[{2# - 1, 2# - 1} &, 37] (* Robert G. Wilson v, Jul 07 2012 *)

PROG

(Haskell)

a109613 = (+ 1) . (* 2) . (`div` 2)

a109613_list = 1 : 1 : map (+ 2) a109613_list

-- Reinhard Zumkeller, Oct 27 2012, Feb 21 2011

(PARI) A109613(n)=n>>1<<1+1 \\ Charles R Greathouse IV, Feb 24, 2011

(Sage) def a(n) : return( len( CuspForms( Gamma0( 5), 2*n + 4, prec=1). basis())); # Michael Somos, May 29 2013

CROSSREFS

Cf. A063196, A110660, A186421, A186422, A211955, A230584, A290988.

Complement of A052928 with respect to the universe A004526. - Guenther Schrack, Aug 21 2018

First differences of A000982, A061925, A074148, A105343, A116940, and A179207. - Guenther Schrack, Aug 21 2018

Sequence in context: A296063 A127630 A267458 * A063196 A245150 A237718

Adjacent sequences:  A109610 A109611 A109612 * A109614 A109615 A109616

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Aug 01 2005

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 12 23:01 EST 2018. Contains 318081 sequences. (Running on oeis4.)