login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A238406 Number T(n,k) of partitions of n into k parts such that every i-th smallest part (counted with multiplicity) is different from i; triangle T(n,k), n>=0, 0<=k<=floor((sqrt(9+8*n)-3)/2) read by rows. 10
1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 3, 0, 1, 3, 1, 0, 1, 4, 3, 0, 1, 4, 4, 0, 1, 5, 6, 0, 1, 5, 7, 0, 1, 6, 9, 1, 0, 1, 6, 11, 4, 0, 1, 7, 13, 7, 0, 1, 7, 15, 11, 0, 1, 8, 18, 15, 0, 1, 8, 20, 19, 0, 1, 9, 23, 25, 1, 0, 1, 9, 26, 30, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,14

LINKS

Alois P. Heinz, Rows n = 0..500, flattened

EXAMPLE

T(10,1) = 1: [10].

T(10,2) = 4: [5,5], [4,6], [3,7], [2,8].

T(10,3) = 3: [3,3,4], [2,4,4], [2,3,5].

Triangle T(n,k) begins:

1;

0;

0, 1;

0, 1;

0, 1;

0, 1, 1;

0, 1, 2;

0, 1, 2;

0, 1, 3;

0, 1, 3, 1;

0, 1, 4, 3;

0, 1, 4, 4;

0, 1, 5, 6;

0, 1, 5, 7;

0, 1, 6, 9, 1;

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1,

`if`(i<1, 0, b(n, i-1)+`if`(i>n, 0, (p-> expand(

x*(p-coeff(p, x, i-1)*x^(i-1))))(b(n-i, i)))))

end:

T:= n-> (p-> seq(coeff(p, x, i), i=0..max(0, degree(p))))(b(n$2)):

seq(T(n), n=0..30);

MATHEMATICA

b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, Function[p, Expand[x*(p - Coefficient[p, x, i-1]*x^(i-1))]][b[n-i, i]]]] ]; T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, Max[0, Exponent[p, x]]}]][b[n, n]]; Table[T[n], {n, 0, 30}] // Flatten (* Jean-François Alcover, Feb 08 2017, translated from Maple *)

CROSSREFS

Columns k=0-10 give: A000007, A000012 (for n>1), A004526(n-2) (for n>4), A244239, A244240, A244241, A244242, A244243, A244244, A244245, A244246.

Row sums give A238394.

Cf. A052146.

Sequence in context: A163325 A105186 A328346 * A058709 A025842 A141100

Adjacent sequences: A238403 A238404 A238405 * A238407 A238408 A238409

KEYWORD

nonn,tabf,look

AUTHOR

Alois P. Heinz, Feb 26 2014

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 29 13:10 EST 2023. Contains 359923 sequences. (Running on oeis4.)