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 A291904 Triangle read by rows: T(n,k) = T(n-k,k-1) + T(n-k,k+1) with T(0,0) = 1 for 0 <= k <= A003056(n). 3
 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 0, 2, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 3, 2, 0, 0, 3, 2, 1, 1, 1, 0, 2, 3, 2, 1, 0, 0, 3, 4, 3, 1, 0, 0, 4, 4, 3, 2, 1, 0, 4, 6, 4, 2, 0, 0, 6, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,38 LINKS Seiichi Manyama, Rows n = 0..481, flattened EXAMPLE First few rows are:   1;   0, 1;   0, 0;   0, 0, 1;   0, 1, 0;   0, 0, 0;   0, 0, 1, 1;   0, 1, 0, 0;   0, 0, 1, 0;   0, 1, 1, 1;   0, 1, 0, 0, 1;   0, 0, 2, 1, 0;   0, 2, 1, 1, 0. MATHEMATICA T[0, 0] = 1; T[_, 0] = 0; T[n_?Positive, k_] /; 0 < k <= Floor[(Sqrt[8n+1] - 1)/2] := T[n, k] = T[n-k, k-1] + T[n-k, k+1]; T[_, _] = 0; Table[T[n, k], {n, 0, 20}, {k, 0, Floor[(Sqrt[8n+1] - 1)/2]}] // Flatten (* Jean-François Alcover, May 29 2019 *) CROSSREFS Row sums give A291905. Columns 0-1 give A000007, A227310 (for n>0). Cf. A008289, A291895, A291929. Sequence in context: A054008 A125676 A291955 * A249808 A258453 A025874 Adjacent sequences:  A291901 A291902 A291903 * A291905 A291906 A291907 KEYWORD nonn,tabf AUTHOR Seiichi Manyama, Sep 05 2017 STATUS approved

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Last modified January 20 08:18 EST 2020. Contains 331081 sequences. (Running on oeis4.)