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A214246 Number A(n,k) of compositions of n where differences between neighboring parts are in {-k,0,k}; square array A(n,k), n>=0, k>=0, read by antidiagonals. 10
1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 1, 1, 2, 2, 6, 2, 1, 1, 2, 2, 5, 11, 4, 1, 1, 2, 2, 3, 5, 17, 2, 1, 1, 2, 2, 3, 4, 10, 29, 4, 1, 1, 2, 2, 3, 2, 7, 10, 47, 3, 1, 1, 2, 2, 3, 2, 6, 8, 21, 78, 4, 1, 1, 2, 2, 3, 2, 4, 5, 9, 22, 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) = 5: [5], [3,1,1], [1,3,1], [1,1,3], [1,1,1,1,1].

A(6,3) = 7: [6], [4,1,1], [3,3], [2,2,2], [1,4,1], [1,1,4], [1,1,1,1,1,1].

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,  2,  2,  2,  2,  2,  2, ...

3,  6,  5,  3,  3,  3,  3,  3, ...

2, 11,  5,  4,  2,  2,  2,  2, ...

4, 17, 10,  7,  6,  4,  4,  4, ...

2, 29, 10,  8,  5,  4,  2,  2, ...

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, 0, 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, Union[{-k, 0, 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

Column k=0 and diagonal give: A000005.

Columns k=1, 2 give: A034297, A214253.

Cf. A214247, A214248, A214249, A214257, A214258, A214268, A214269.

Sequence in context: A138015 A103444 A099172 * A214257 A214248 A152719

Adjacent sequences:  A214243 A214244 A214245 * A214247 A214248 A214249

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Jul 08 2012

STATUS

approved

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Last modified September 2 22:02 EDT 2014. Contains 246369 sequences.