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A206464 Number of length-n Catalan-RGS (restricted growth strings) such that the RGS is a valid mixed radix number in falling factorial basis. 3
1, 1, 2, 4, 10, 26, 74, 218, 672, 2126, 6908, 22876, 77100, 263514, 911992, 3189762, 11261448, 40083806, 143713968, 518594034, 1882217168, 6867064856, 25172021144, 92666294090, 342467464612, 1270183943200, 4726473541216, 17640820790092, 66025467919972 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Catalan-RGS are strings with first digit d(0)=zero, and d(k+1) <= d(k)+1, falling factorial mixed radix numbers have last digit <=1, second last <=2, etc.

The digits of the RGS are <= floor(n/2).

The first few terms are the same as for A089429.

Column k=0 of A264869. - Peter Bala, Nov 27 2015

a(n) = A291680(n+1,n+1). - Alois P. Heinz, Aug 29 2017

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

Conjecture: a(n) = Sum_{k = 0..floor(n/4)} (-1)^k * C(floor(n/2) + 1 - k, k + 1) * a(n - 1 - k), a(0) = 1. - Gionata Neri, Jun 17 2018

EXAMPLE

The a(5)=26 strings for n=5 are (dots for zeros):

   1:  [ . . . . . ]

   2:  [ . . . . 1 ]

   3:  [ . . . 1 . ]

   4:  [ . . . 1 1 ]

   5:  [ . . 1 . . ]

   6:  [ . . 1 . 1 ]

   7:  [ . . 1 1 . ]

   8:  [ . . 1 1 1 ]

   9:  [ . . 1 2 . ]

  10:  [ . . 1 2 1 ]

  11:  [ . 1 . . . ]

  12:  [ . 1 . . 1 ]

  13:  [ . 1 . 1 . ]

  14:  [ . 1 . 1 1 ]

  15:  [ . 1 1 . . ]

  16:  [ . 1 1 . 1 ]

  17:  [ . 1 1 1 . ]

  18:  [ . 1 1 1 1 ]

  19:  [ . 1 1 2 . ]

  20:  [ . 1 1 2 1 ]

  21:  [ . 1 2 . . ]

  22:  [ . 1 2 . 1 ]

  23:  [ . 1 2 1 . ]

  24:  [ . 1 2 1 1 ]

  25:  [ . 1 2 2 . ]

  26:  [ . 1 2 2 1 ]

MAPLE

b:= proc(i, l) option remember;

      `if`(i<=0, 1, add(b(i-1, j), j=0..min(l+1, i)))

    end:

a:= n-> b(n-1, 0):

seq(a(n), n=0..40);  # Alois P. Heinz, Feb 08 2012

CROSSREFS

Cf. A080935, A080936, A264869, A291680.

Sequence in context: A279544 A245898 A230662 * A089429 A049143 A089404

Adjacent sequences:  A206461 A206462 A206463 * A206465 A206466 A206467

KEYWORD

nonn

AUTHOR

Joerg Arndt, Feb 08 2012

STATUS

approved

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Last modified October 17 05:23 EDT 2018. Contains 316275 sequences. (Running on oeis4.)