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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A130780 Number of partitions of n such that number of odd parts is greater than or equal to number of even parts. 8
1, 1, 1, 3, 3, 6, 8, 12, 16, 23, 32, 42, 58, 75, 102, 131, 173, 220, 288, 363, 466, 587, 743, 929, 1164, 1448, 1797, 2224, 2738, 3368, 4122, 5042, 6133, 7466, 9035, 10941, 13184, 15888, 19064, 22876, 27343 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) = A108950(n) + A045931(n) = A000041(n) - A108949(n). - Reinhard Zumkeller, Jan 21 2010

a(n) = Sum_{k=0..n} A240009(n,k). - Alois P. Heinz, Mar 30 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

FORMULA

G.f.: Sum_{k>=0} x^k/Product_{i=1..k} (1-x^(2*i))^2.

EXAMPLE

a(5)=6 because we have 5,41,32,311,211 and 11111 (221 does not qualify).

MAPLE

g:=sum(x^k/(product((1-x^(2*i))^2, i=1..k)), k=0..50): gser:=series(g, x=0, 50): seq(coeff(gser, x, n), n=1..40); - Emeric Deutsch, Aug 24 2007

# second Maple program:

b:= proc(n, i, t) option remember; `if`(n=0,

      `if`(t>=0, 1, 0), `if`(i<1, 0, b(n, i-1, t)+

      `if`(i>n, 0, b(n-i, i, t+(2*irem(i, 2)-1)))))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..80);  # Alois P. Heinz, Mar 30 2014

MATHEMATICA

$RecursionLimit = 1000; b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t >= 0, 1, 0],  If[i<1, 0, b[n, i-1, t] + If[i>n, 0, b[n-i, i, t + (2*Mod[i, 2]-1)]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 80}] (* Jean-Fran├žois Alcover, May 12 2015, after Alois P. Heinz  *)

CROSSREFS

Cf. A045931, A108949, A108950.

Cf. A171966, A171967. - Reinhard Zumkeller, Jan 21 2010

Sequence in context: A241390 A241831 A239946 * A174524 A143592 A280197

Adjacent sequences:  A130777 A130778 A130779 * A130781 A130782 A130783

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Aug 19 2007

EXTENSIONS

More terms from Emeric Deutsch, Aug 24 2007

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 28 08:24 EDT 2017. Contains 288813 sequences.