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!)
A239550 Number A(n,k) of compositions of n such that the first part is 1 and the second differences of the parts are in {-k,...,k}; square array A(n,k), n>=0, k>=0, read by antidiagonals. 13
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, 4, 4, 3, 1, 1, 1, 2, 4, 7, 6, 2, 1, 1, 1, 2, 4, 7, 11, 9, 2, 1, 1, 1, 2, 4, 8, 13, 18, 13, 3, 1, 1, 1, 2, 4, 8, 15, 23, 32, 18, 3, 1, 1, 1, 2, 4, 8, 15, 28, 40, 53, 24, 2, 1, 1, 1, 2, 4, 8, 16, 29, 52, 73, 89, 34, 3 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,10

LINKS

Alois P. Heinz, Antidiagonals n = 0..140, flattened

EXAMPLE

A(6,0) = 3: [1,1,1,1,1,1], [1,2,3], [1,5].

A(5,1) = 4: [1,1,1,1,1], [1,1,1,2], [1,2,2], [1,4].

A(4,2) = 4: [1,1,1,1], [1,1,2], [1,2,1], [1,3].

Square array A(n,k) begins:

  1,  1,  1,  1,  1,  1,  1,  1,  1, ...

  1,  1,  1,  1,  1,  1,  1,  1,  1, ...

  1,  1,  1,  1,  1,  1,  1,  1,  1, ...

  2,  2,  2,  2,  2,  2,  2,  2,  2, ...

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

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

  3,  6, 11, 13, 15, 15, 16, 16, 16, ...

  2,  9, 18, 23, 28, 29, 31, 31, 32, ...

  2, 13, 32, 40, 52, 56, 60, 61, 63, ...

MAPLE

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

      `if`(i=0, add(b(n-h, j, h, k), h=1..n), add(

       b(n-h, j, h, k), h=max(1, 2*j-i-k)..min(n, 2*j-i+k))))

    end:

A:= (n, k)-> `if`(n=0, 1, b(n-1, 0, 1, k)):

seq(seq(A(n, d-n), n=0..d), d=0..12);

MATHEMATICA

b[n_, i_, j_, k_] := b[n, i, j, k] = If[n == 0, 1, If[i == 0, Sum[b[n-h, j, h, k], {h, 1, n}], Sum[b[n-h, j, h, k], {h, Max[1, 2*j - i - k], Min[n, 2*j - i + k]}]]] ; A[n_, k_] := If[n == 0, 1, b[n-1, 0, 1, k]]; Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-Fran├žois Alcover, Jan 22 2015, after Alois P. Heinz *)

CROSSREFS

Columns k=0-10 gives: A129654, A239551, A239552, A239553, A239554, A239555, A239556, A239557, A239558, A239559, A239560.

Main diagonal gives A239561.

Sequence in context: A276317 A289944 A055215 * A058398 A091499 A284249

Adjacent sequences:  A239547 A239548 A239549 * A239551 A239552 A239553

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Mar 21 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)