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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A026833 Number of partitions of n into distinct parts, the least being even. 2
0, 0, 1, 0, 1, 1, 2, 1, 2, 3, 4, 4, 5, 6, 8, 9, 11, 14, 16, 18, 22, 26, 31, 36, 42, 49, 57, 66, 76, 88, 102, 116, 134, 154, 176, 201, 229, 260, 296, 336, 381, 432, 488, 550, 622, 700, 788, 886, 994, 1115, 1250, 1399, 1564, 1748, 1952, 2176, 2426, 2701, 3004 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Also number of partitions of n such that if k is the largest part, then k occurs an even number of times and each of the numbers 1,2,...,k-1 occurs at least once. Example: a(10)=4 because we have [3,3,2,1,1], [2,2,2,2,1,1], [2,2,1,1,1,1,1,1] and [1,1,1,1,1,1,1,1,1,1]. - Emeric Deutsch, Mar 30 2006

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: Sum_{k>=2} ((-1)^k*(-1+Product_{i>=k} (1+x^i))). - Vladeta Jovovic, Aug 26 2003

G.f.: Sum_{k>=1} x^(2k)*Product_{j>=2k+1} (1+x^j).

G.f.: Sum_{k>=1} x^(k*(k+3)/2)/((1+x^k)*Product_{j=1..k} (1-x^j)). - Emeric Deutsch, Mar 30 2006

a(n) ~ exp(Pi*sqrt(n/3)) / (4 * 3^(5/4) * n^(3/4)). - Vaclav Kotesovec, Jun 09 2019

EXAMPLE

a(10)=4 because we have [10], [8,2], [6,4] and [5,3,2].

MAPLE

g:=sum(x^(2*k)*product(1+x^j, j=2*k+1..60), k=1..60): gser:=series(g, x=0, 58): seq(coeff(gser, x, n), n=0..55); # Emeric Deutsch, Mar 30 2006

# second Maple program:

b:= proc(n, i) option remember; `if`(i*(i+1)/2-1<n, 0, b(n, i-1)+

      `if`(i=n and i::even, 1, 0)+`if`(i<n, b(n-i, min(n-i, i-1)), 0))

    end:

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

seq(a(n), n=0..60);  # Alois P. Heinz, Feb 01 2019

CROSSREFS

Cf. A026832.

Sequence in context: A031231 A030562 A238219 * A281544 A056882 A035534

Adjacent sequences:  A026830 A026831 A026832 * A026834 A026835 A026836

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

a(0)=0 prepended by Alois P. Heinz, Feb 01 2019

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 August 22 12:18 EDT 2019. Contains 326177 sequences. (Running on oeis4.)