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 A209972 Number of binary words of length n avoiding the subword given by the binary expansion of k; square array A(n,k), n>=0, k>=0, read by antidiagonals. 10
 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 4, 1, 1, 1, 2, 4, 5, 5, 1, 1, 1, 2, 4, 7, 8, 6, 1, 1, 1, 2, 4, 7, 12, 13, 7, 1, 1, 1, 2, 4, 7, 12, 20, 21, 8, 1, 1, 1, 2, 4, 7, 12, 21, 33, 34, 9, 1, 1, 1, 2, 4, 8, 13, 20, 37, 54, 55, 10, 1, 1, 1, 2, 4, 8, 15, 24, 33, 65, 88, 89, 11, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Alois P. Heinz, Antidiagonals n = 0..150, flattened EXAMPLE Square array begins: 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 1, 2, 2, 2, 2, 2, 2, 2, ... 1, 1, 3, 3, 4, 4, 4, 4, 4, ... 1, 1, 4, 5, 7, 7, 7, 7, 8, ... 1, 1, 5, 8, 12, 12, 12, 13, 15, ... 1, 1, 6, 13, 20, 21, 20, 24, 28, ... 1, 1, 7, 21, 33, 37, 33, 44, 52, ... 1, 1, 8, 34, 54, 65, 54, 81, 96, ... 1, 1, 9, 55, 88, 114, 88, 149, 177, ... MATHEMATICA A[n_, k_] := Module[{bb, cnt = 0}, Do[bb = PadLeft[IntegerDigits[j, 2], n]; If[SequencePosition[bb, IntegerDigits[k, 2], 1]=={}, cnt++], {j, 0, 2^n-1 }]; cnt]; Table[A[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Nov 01 2021 *) CROSSREFS Columns give: 0, 1: A000012, 2: A001477(n+1), 3: A000045(n+2), 4, 6: A000071(n+3), 5: A005251(n+3), 7: A000073(n+3), 8, 12, 14: A008937(n+1), 9, 11, 13: A049864(n+2), 10: A118870, 15: A000078(n+4), 16, 20, 24, 26, 28, 30: A107066, 17, 19, 23, 25, 29: A210003, 18, 22: A209888, 21: A152718(n+3), 27: A210021, 31: A001591(n+5), 32: A001949(n+5), 33, 35, 37, 39, 41, 43, 47, 49, 53, 57, 61: A210031. Main diagonal equals A234005 or column k=0 of A233940. Sequence in context: A245563 A356917 A122945 * A205573 A119338 A054124 Adjacent sequences: A209969 A209970 A209971 * A209973 A209974 A209975 KEYWORD nonn,tabl,base AUTHOR Alois P. Heinz, Mar 16 2012 STATUS approved

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Last modified December 7 04:15 EST 2023. Contains 367629 sequences. (Running on oeis4.)