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!)
A214268 Number A(n,k) of compositions of n where the difference between largest and smallest parts is <= k and adjacent parts are unequal; square array A(n,k), n>=0, k>=0, read by antidiagonals. 8
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 3, 4, 4, 1, 1, 1, 1, 3, 4, 5, 3, 1, 1, 1, 1, 3, 4, 7, 11, 5, 1, 1, 1, 1, 3, 4, 7, 12, 12, 3, 1, 1, 1, 1, 3, 4, 7, 14, 20, 16, 5, 1, 1, 1, 1, 3, 4, 7, 14, 21, 28, 30, 5, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,14

LINKS

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

EXAMPLE

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

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

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

A(6,3) = 12: [6], [4,2], [3,2,1], [3,1,2], [2,4], [2,3,1], [2,1,3], [2,1,2,1], [1,4,1], [1,3,2], [1,2,3], [1,2,1,2].

A(7,4) = 21: [7], [5,2], [4,3], [4,2,1], [4,1,2], [3,4], [3,1,3], [3,1,2,1], [2,5], [2,4,1], [2,3,2], [2,1,4], [2,1,3,1], [1,5,1], [1,4,2], [1,3,2,1], [1,3,1,2], [1,2,4], [1,2,3,1], [1,2,1,3], [1,2,1,2,1].

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,  3,  3,  3,  3,  3,  3,  3, ...

  1,  2,  4,  4,  4,  4,  4,  4, ...

  1,  4,  5,  7,  7,  7,  7,  7, ...

  1,  3, 11, 12, 14, 14, 14, 14, ...

  1,  5, 12, 20, 21, 23, 23, 23, ...

MAPLE

b:= proc(n, k, s, t, l) option remember;

      `if`(n<0, 0, `if`(n=0, 1, add(`if`(j=l, 0, b(n-j, k,

       min(s, j), max(t, j), j)), j=max(1, t-k+1)..s+k-1)))

    end:

A:= (n, k)-> `if`(n=0, 1, add(b(n-j, k+1, j, j, j), j=1..n)):

seq(seq(A(n, d-n), n=0..d), d=0..14);

MATHEMATICA

b[n_, k_, s_, t_, l_] := b[n, k, s, t, l] = If[n < 0, 0, If[n == 0, 1, Sum[If[j == l, 0, b[n - j, k, Min[s, j], Max[t, j], j]], {j, Max[1, t - k + 1], s + k - 1}]]]; A[n_, k_] := If[n == 0, 1, Sum[b[n - j, k + 1, j, j, j], {j, 1, n}]]; Table[Table[A [n, d - n], {n, 0, d}], {d, 0, 14}] // Flatten (* Jean-Fran├žois Alcover, Dec 27 2013, translated from Maple *)

CROSSREFS

Columns k=0, 1 give: A000012, 1+A214270(n).

Main diagonal gives: A003242.

Cf. A214246, A214247, A214248, A214249, A214257, A214258, A214269.

Sequence in context: A256452 A330827 A010276 * A214249 A271714 A049639

Adjacent sequences:  A214265 A214266 A214267 * A214269 A214270 A214271

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Jul 09 2012

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 July 12 16:37 EDT 2020. Contains 335665 sequences. (Running on oeis4.)