login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A179647 Rectangular array read by antidiagonals: T(n,k) is the number of compositions (ordered partitions) of n in which no part (summand) is equal to k. 1
0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 3, 4, 3, 1, 2, 4, 6, 7, 5, 1, 2, 4, 7, 11, 12, 8, 1, 2, 4, 8, 14, 21, 21, 13, 1, 2, 4, 8, 15, 27, 39, 37, 21, 1, 2, 4, 8, 16, 30, 52, 73, 65, 34, 1, 2, 4, 8, 16, 31, 59, 101, 136, 114, 55, 1, 2, 4, 8, 16, 32, 62, 116, 195, 254, 200, 89 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Alois P. Heinz, Antidiagonals n = 1..141, flattened

FORMULA

O.g.f. for column k: B(A(x)) where A(x) = x/(1-x)-x^k and B(x) = 1/(1-x).

EXAMPLE

T(4,2) = 4 because there are four compositions of 4 with no part equal to two: 4, 3+1, 1+3, 1+1+1+1.

Array starts as:

0,    1,   1,   1,   1,   1,   1,   1,   1,   1, ...

1,    1,   2,   2,   2,   2,   2,   2,   2,   2, ...

1,    2,   3,   4,   4,   4,   4,   4,   4,   4, ...

2,    4,   6,   7,   8,   8,   8,   8,   8,   8, ...

3,    7,  11,  14,  15,  16,  16,  16,  16,  16, ...

5,   12,  21,  27,  30,  31,  32,  32,  32,  32, ...

8,   21,  39,  52,  59,  62,  63,  64,  64,  64, ...

13,  37,  73, 101, 116, 123, 126, 127, 128, 128, ...

21,  65, 136, 195, 228, 244, 251, 254, 255, 256, ...

34, 114, 254, 377, 449, 484, 500, 507, 510, 511, ...

MAPLE

T:= proc(n, k) option remember;

      `if`(n=0, 1, add(`if`(j=k, 0, T(n-j, k)), j=1..n))

    end:

seq(seq(T(n, d+1-n), n=1..d), d=1..12);  # Alois P. Heinz, Oct 23 2011

MATHEMATICA

Transpose[Table[Table[Length[Select[Level[Map[Permutations, IntegerPartitions[n]], {2}], FreeQ[#, i] &]], {n, 1, 10}], {i, 1, 10}]] // Grid

(* second program: *)

a = x/(1 - x) - x^n; Transpose[Table[Rest[CoefficientList[Series[1/(1 - a), {x, 0, 10}], x]], {n, 1, 10}]] // Grid

CROSSREFS

Sequence in context: A261904 A297030 A266348 * A029330 A132225 A263923

Adjacent sequences:  A179644 A179645 A179646 * A179648 A179649 A179650

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Jan 09 2011

EXTENSIONS

Corrected and extended by Alois P. Heinz, Oct 23 2011

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 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)