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 A214249 Number A(n,k) of compositions of n where differences between neighboring parts are in {-k,...,k} \ {0}; square array A(n,k), n>=0, k>=0, read by antidiagonals. 10
 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, 5, 1, 1, 1, 1, 3, 4, 7, 11, 5, 1, 1, 1, 1, 3, 4, 7, 12, 14, 7, 1, 1, 1, 1, 3, 4, 7, 14, 20, 18, 10, 1, 1, 1, 1, 3, 4, 7, 14, 21, 30, 36, 9, 1, 1, 1, 1, 3, 4, 7, 14, 23, 36, 50, 49, 14, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,14 LINKS Alois P. Heinz, Rows n = 0..140, flattened 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]. 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,  5, 11, 12, 14, 14, 14, 14, ...   1,  5, 14, 20, 21, 23, 23, 23, ... 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} minus{0})))     end: A:= (n, k)-> `if`(n=0, 1, add(b(n, j, min(n, 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, Range[-k, -1] ~Join~ Range[k]}]]]; A[n_, k_] := If[n == 0, 1, Sum[b[n, j, Min[n, k]], {j, 1, n}]]; Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 15}] // Flatten (* Jean-François Alcover, Jan 15 2014, translated from Maple *) CROSSREFS Columns k=0-2 give: A000012, A173258, A214256. Main diagonal gives: A003242. Cf. A214246, A214247, A214248, A214257, A214258, A214268, A214269. Sequence in context: A330827 A010276 A214268 * A271714 A049639 A046555 Adjacent sequences:  A214246 A214247 A214248 * A214250 A214251 A214252 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Jul 08 2012 STATUS approved

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Last modified June 3 05:29 EDT 2020. Contains 334798 sequences. (Running on oeis4.)