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A109613 Odd numbers repeated. 61
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(a(k)*a(n-k): 0<=k<=n);

A167875(n) = SUM(a(k)*A005408(n-k): 0<=k<=n);

A171218(n) = SUM(a(k)*A005843(n-k): 0<=k<=n);

A008794(n+2) = SUM(a(k)*A059841(n-k): 0<=k<=n). (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

LINKS

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

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

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.

Cf. A230584, A290988.

Sequence in context: A117767 A127630 A267458 * A063196 A245150 A237718

Adjacent sequences:  A109610 A109611 A109612 * A109614 A109615 A109616

KEYWORD

nonn,easy,changed

AUTHOR

Reinhard Zumkeller, Aug 01 2005

STATUS

approved

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Last modified August 24 06:49 EDT 2017. Contains 291052 sequences.