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 A214247 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. 11
 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 3, 4, 4, 1, 1, 1, 1, 1, 2, 5, 2, 1, 1, 1, 1, 1, 3, 3, 5, 4, 1, 1, 1, 1, 1, 1, 2, 2, 7, 3, 1, 1, 1, 1, 1, 1, 3, 3, 6, 10, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 9, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Alois P. Heinz, Antidiagonals n = 0..140 EXAMPLE A(5,0) = 2: [5], [1,1,1,1,1]. A(5,1) = 4: [5], [3,2], [2,3], [2,1,2]. A(5,2) = 2: [5], [1,3,1]. A(5,3) = 3: [5], [4,1], [1,4]. Square array A(n,k) begins:   1,  1,  1,  1,  1,  1,  1,  1, ...   1,  1,  1,  1,  1,  1,  1,  1, ...   2,  1,  1,  1,  1,  1,  1,  1, ...   2,  3,  1,  1,  1,  1,  1,  1, ...   3,  2,  3,  1,  1,  1,  1,  1, ...   2,  4,  2,  3,  1,  1,  1,  1, ...   4,  5,  3,  2,  3,  1,  1,  1, ...   2,  5,  2,  3,  2,  3,  1,  1, ... 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, Union[{-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-François Alcover, Dec 13 2013, translated from Maple *) CROSSREFS Columns k=0-2 give: A000005, A173258, A214254. Rows n=0, 1 and main diagonal give: A000012. Cf. A214246, A214248, A214249, A214257, A214258, A214268, A214269. Sequence in context: A143654 A170981 A161096 * A211987 A165983 A300719 Adjacent sequences:  A214244 A214245 A214246 * A214248 A214249 A214250 KEYWORD nonn,tabl,look AUTHOR Alois P. Heinz, Jul 08 2012 STATUS approved

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Last modified May 25 07:29 EDT 2020. Contains 334584 sequences. (Running on oeis4.)