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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.)