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

 

Logo

The submissions stack has been unacceptably high for several months now. Please voluntarily restrict your submissions and please help with the editing. (We don't want to have to impose further limits.)

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A116679 Triangle read by rows: T(n,k) is the number of partitions of n into distinct part and having exactly k even parts (n>=0, k>=0). 1
1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 2, 3, 1, 2, 4, 2, 2, 5, 3, 2, 6, 4, 3, 7, 4, 1, 3, 8, 6, 1, 3, 10, 8, 1, 4, 11, 10, 2, 5, 13, 11, 3, 5, 15, 14, 4, 5, 18, 18, 5, 6, 20, 21, 7, 7, 23, 24, 9, 1, 8, 26, 29, 12, 1, 8, 30, 36, 14, 1, 9, 34, 41, 18, 2, 11, 38, 47, 23, 3, 12, 43, 55, 28, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

Row n contains floor((1+sqrt(1+4n))/2) terms. Row sums yield A000009. T(n,0)=A000700(n). T(n,1)=A096911(n) (n>=1). Sum(k*T(n,k), k>=0)=A116680(n).

LINKS

Table of n, a(n) for n=0..89.

FORMULA

G.f.=product((1+x^(2j-1))(1+tx^(2j)), j=1..infinity).

EXAMPLE

T(9,2)=2 because we have [6,2,1] and [4,3,2].

Triangle starts:

1;

1;

0,1;

1,1;

1,1;

1,2;

1,2,1;

1,3,1;

MAPLE

g:=product((1+x^(2*j-1))*(1+t*x^(2*j)), j=1..25): gser:=simplify(series(g, x=0, 38)): P[0]:=1: for n from 1 to 27 do P[n]:=sort(coeff(gser, x^n)) od: for n from 0 to 27 do seq(coeff(P[n], t, j), j=0..floor((sqrt(1+4*n)-1)/2)) od; # yields sequence in triangular form

CROSSREFS

Cf. A000009, A000700, A096911, A116680.

Sequence in context: A233932 A008289 A188884 * A146290 A135539 A240060

Adjacent sequences:  A116676 A116677 A116678 * A116680 A116681 A116682

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, Feb 22 2006

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified August 29 01:49 EDT 2015. Contains 261184 sequences.