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 A094718 Array T read by antidiagonals: T(n,k) = number of involutions avoiding 132 and 12...k. 11
 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 2, 1, 0, 1, 2, 3, 4, 1, 0, 1, 2, 3, 5, 4, 1, 0, 1, 2, 3, 6, 8, 8, 1, 0, 1, 2, 3, 6, 9, 13, 8, 1, 0, 1, 2, 3, 6, 10, 18, 21, 16, 1, 0, 1, 2, 3, 6, 10, 19, 27, 34, 16, 1, 0, 1, 2, 3, 6, 10, 20, 33, 54, 55, 32, 1, 0, 1, 2, 3, 6, 10, 20, 34, 61, 81, 89, 32, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Also, number of paths along a corridor with width k, starting from one side (from H. Bottomley's comment in A061551). Rows converge to binomial(n,floor(n/2)) (A001405). LINKS O. Guibert and T. Mansour, Restricted 132-involutions, Séminaire Lotharingien de Combinatoire, B48a (2002), 23 pp. T. Mansour, Restricted even permutations and Chebyshev polynomials, arXiv:math/0302014 [math.CO], 2003. FORMULA G.f. for k-th row: 1/(xU(k, 1/(2x))) * Sum_{j=0..k-1} U(j, 1/(2x)), with U(k, x) the Chebyshev polynomials of second kind. - N. J. A. Sloane, Dec 20 2008; corrected by Jean-François Alcover, Nov 17 2018 EXAMPLE Array begins   0   0   0   0   0   0   0   0   0   0 ...   1   1   1   1   1   1   1   1   1   1 ...   1   2   2   4   4   8   8  16  16  32 ...   1   2   3   5   8  13  21  34  55  89 ...   1   2   3   6   9  18  27  54  81 162 ...   1   2   3   6  10  19  33  61 108 197 ...   1   2   3   6  10  20  34  68 116 232 ...   1   2   3   6  10  20  35  69 124 241 ...   1   2   3   6  10  20  35  70 125 250 ...   1   2   3   6  10  20  35  70 126 251 ...   ... MATHEMATICA U = ChebyshevU; m = maxExponent = 14; row[1] = Array[0&, m]; row[k_] := 1/(x U[k, 1/(2x)])*Sum[U[j, 1/(2x)], {j, 0, k-1}] + O[x]^m // CoefficientList[#, x]& // Rest; T = Table[row[n], {n, 1, m}]; Table[T[[n-k+1, k]], {n, 1, m-1}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 17 2018 *) CROSSREFS Rows 3-8 are A016116, A000045, A038754, A028495, A030436, A061551. Main diagonal is A014495, antidiagonal sums are in A094719. Cf. A080934 (permutations). Sequence in context: A239287 A305258 A053616 * A076191 A282318 A286971 Adjacent sequences:  A094715 A094716 A094717 * A094719 A094720 A094721 KEYWORD nonn,tabl AUTHOR Ralf Stephan, May 23 2004 STATUS approved

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Last modified October 14 03:00 EDT 2019. Contains 327995 sequences. (Running on oeis4.)