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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 C(n,[n/2]) (A001405).

LINKS

Table of n, a(n) for n=1..90.

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. [Probably "1/2x" is intended to mean "x/2". - N. J. A. Sloane, Dec 20 2008]

EXAMPLE

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

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 19 16:58 EDT 2018. Contains 316368 sequences. (Running on oeis4.)