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A214248 Number A(n,k) of compositions of n where differences between neighboring parts are in {-k,...,k}; square array A(n,k), n>=0, k>=0, read by antidiagonals. 12
1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 1, 1, 2, 4, 6, 2, 1, 1, 2, 4, 8, 11, 4, 1, 1, 2, 4, 8, 14, 17, 2, 1, 1, 2, 4, 8, 16, 27, 29, 4, 1, 1, 2, 4, 8, 16, 30, 49, 47, 3, 1, 1, 2, 4, 8, 16, 32, 59, 92, 78, 4, 1, 1, 2, 4, 8, 16, 32, 62, 113, 170, 130, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

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

EXAMPLE

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

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

A(5,2) = 14: [5], [3,2], [3,1,1], [2,3], [2,2,1], [2,1,2], [2,1,1,1], [1,3,1], [1,2,2], [1,2,1,1], [1,1,3], [1,1,2,1], [1,1,1,2], [1,1,1,1,1].

Square array A(n,k) begins:

  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,  4,  4,  4,  4,  4,  4,  4, ...

  3,  6,  8,  8,  8,  8,  8,  8, ...

  2, 11, 14, 16, 16, 16, 16, 16, ...

  4, 17, 27, 30, 32, 32, 32, 32, ...

  2, 29, 49, 59, 62, 64, 64, 64, ...

MAPLE

b:= proc(n, i, k) option remember;

      `if`(n<1 or i<1, 0, `if`(n=i, 1, add(b(n-i, i+j, k), j={$-k..k})))

    end:

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

seq(seq(A(n, d-n), n=0..d), d=0..15);

MATHEMATICA

b[n_, i_, k_] := b[n, i, k] = If[n < 1 || i < 1, 0, If[n == i, 1, Sum[b[n - i, i + j, k], {j, -k, k}]]]; A[n_, k_] := If[n == 0, 1, Sum[b[n, j, k], {j, 1, n}]]; Table[Table[A[n, d - n], {n, 0, d}], {d, 0, 15}] // Flatten (* Jean-Fran├žois Alcover, Dec 27 2013, translated from Maple *)

CROSSREFS

Columns k=0-2 give: A000005, A034297, A214255.

Main diagonal gives: A011782.

Cf. A214246, A214247, A214249, A214257, A214258, A214268, A214269.

Sequence in context: A099172 A214246 A214257 * A152719 A107044 A141591

Adjacent sequences:  A214245 A214246 A214247 * A214249 A214250 A214251

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Jul 08 2012

STATUS

approved

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Last modified September 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)