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Revision History for A110319 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
Triangle read by rows: T(n,k) (1 <= k <= n) is number of RNA secondary structures of size n (i.e., with n nodes) having k blocks (an RNA secondary structure can be viewed as a restricted noncrossing partition).
(history; published version)
#17 by Bruno Berselli at Fri Jul 06 09:47:12 EDT 2018
STATUS

proposed

approved

#16 by Jean-François Alcover at Fri Jul 06 09:34:37 EDT 2018
STATUS

editing

proposed

#15 by Jean-François Alcover at Fri Jul 06 09:34:34 EDT 2018
MATHEMATICA

T[n_, k_] := (1/k)*Binomial[k, n - k]*Binomial[k, n - k + 1];

Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jul 06 2018, from Maple *)

STATUS

approved

editing

#14 by Joerg Arndt at Tue Feb 27 12:41:52 EST 2018
STATUS

proposed

approved

#13 by Michel Marcus at Tue Feb 27 12:11:02 EST 2018
STATUS

editing

proposed

#12 by Michel Marcus at Tue Feb 27 12:10:56 EST 2018
EXAMPLE

1;

0, 1;

0, 1, 1;

0, 0, 3, 1;

0, 0, 1, 6, 1;

0, 0, 0, 6, 10, 1;

0, 0, 0, 1, 20, 15, 1;

0, 0, 0, 0, 10, 50, 21, 1;

0, 0, 0, 0, 1, 50, 105, 28, 1;

0, 0, 0, 0, 0, 15, 175, 196, 36, 1;

...

...

STATUS

proposed

editing

#11 by Andrew Howroyd at Tue Feb 27 11:50:46 EST 2018
STATUS

editing

proposed

Discussion
Tue Feb 27
12:09
Michel Marcus: yes bfile was for A110320
#10 by Andrew Howroyd at Tue Feb 27 11:47:01 EST 2018
LINKS

G. C. Greubel, Andrew Howroyd, <a href="/A110320A110319/b110320b110319.txt">Table of n, a(n) for n = 1..10001275</a>

EXAMPLE

Triangle begins:

1;

0, 1;

0, 1, 1;

0, 0, 3, 1;

0, 0, 1, 6, 1;

0, 0, 0, 6, 10, 1;

0, 0, 0, 1, 20, 15, 1;

0, 0, 0, 0, 10, 50, 21, 1;

0, 0, 0, 0, 1, 50, 105, 28, 1;

0, 0, 0, 0, 0, 15, 175, 196, 36, 1;

...

PROG

(PARI) T(n, k) = (1/k)*binomial(k, n-k)*binomial(k, n-k+1); \\ Andrew Howroyd, Feb 27 2018

STATUS

approved

editing

Discussion
Tue Feb 27
11:50
Andrew Howroyd: Existing b-file link is for a different sequence. Cannot find a bfile for this sequence so adding one.
#9 by Joerg Arndt at Sun Jul 23 02:44:28 EDT 2017
STATUS

proposed

approved

#8 by Michel Marcus at Sun Jul 23 02:09:12 EDT 2017
STATUS

editing

proposed