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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-François 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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