The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A206464 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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.
(history; published version)

#43 by Alois P. Heinz at Sat Mar 09 14:23:40 EST 2024

STATUS

proposed

approved

#42 by Jon E. Schoenfield at Sat Mar 09 14:21:33 EST 2024

STATUS

editing

proposed

#41 by Jon E. Schoenfield at Sat Mar 09 14:21:28 EST 2024

NAME

Number of length-n Catalan-RGS (restricted growth strings) such that the RGS is a valid mixed -radix number in falling factorial basis.

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.

STATUS

approved

editing

#40 by Alois P. Heinz at Sat Nov 07 08:45:18 EST 2020

STATUS

proposed

approved

#39 by Jean-François Alcover at Sat Nov 07 08:28:45 EST 2020

STATUS

editing

proposed

#38 by Jean-François Alcover at Sat Nov 07 08:28:41 EST 2020

MATHEMATICA

b[i_, l_] := b[i, l] = If[i <= 0, 1, Sum[b[i-1, j], {j, 0, Min[l+1, i]}]];

a[n_] := b[n-1, 0];

a /@ Range[0, 40] (* Jean-François Alcover, Nov 07 2020, after Alois P. Heinz *)

STATUS

approved

editing

#37 by Bruno Berselli at Mon Jun 18 05:38:34 EDT 2018

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reviewed

approved

#36 by Michel Marcus at Mon Jun 18 05:09:35 EDT 2018

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proposed

reviewed

#35 by Alois P. Heinz at Sun Jun 17 15:10:11 EDT 2018

STATUS

editing

proposed

#34 by Alois P. Heinz at Sun Jun 17 15:09:52 EDT 2018

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

STATUS

proposed

editing