The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A115068

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Showing entries 1-10 | older changes

A115068

Triangle read by rows: T(n,k) = number of elements in the Coxeter group D_n with descent set contained in {s_k}, for 0<=k<=n-1.
(history; published version)

#12 by N. J. A. Sloane at Thu Mar 06 22:33:18 EST 2014

STATUS

reviewed

approved

#11 by Wesley Ivan Hurt at Thu Mar 06 22:26:48 EST 2014

STATUS

proposed

reviewed

#10 by Jon E. Schoenfield at Thu Mar 06 22:17:49 EST 2014

STATUS

editing

proposed

#9 by Jon E. Schoenfield at Thu Mar 06 22:17:47 EST 2014

COMMENTS

A115068 is the fission of the polynomial sequence (p(x,n)) by the polynomial sequence ((2x+1)^n), where p(n,x)=x^n+x^(n-1)+...+x+1, n>=0. See A193842 for the definition of fission. [From - _Clark Kimberling, _, Aug 7 07 2011]

STATUS

approved

editing

#8 by Reinhard Zumkeller at Mon Jul 22 14:12:38 EDT 2013

STATUS

editing

approved

#7 by Reinhard Zumkeller at Mon Jul 22 03:42:46 EDT 2013

LINKS

Reinhard Zumkeller, <a href="/A115068/b115068.txt">Table of n, a(n) for Rows n = 1..7260120 of triangle, flattened</a>

FORMULA

T(n,1) = 2^(n-1), T(n,n) = n, for n > 1: T(n,k) = T(n-1,k-1) + 2*T(n-1,k), 1 < k < n. - Reinhard Zumkeller, Jul 22 2013

PROG

(Haskell)

a115068 n k = a115068_tabl !! (n-1) !! (k-1)

a115068_row n = a115068_tabl !! (n-1)

a115068_tabl = iterate (\row -> zipWith (+) (row ++ [1]) $

zipWith (+) (row ++ [0]) ([0] ++ row)) [1]

-- Reinhard Zumkeller, Jul 22 2013

CROSSREFS

Cf. A105728, A013609.

#6 by Reinhard Zumkeller at Mon Jul 22 03:39:50 EDT 2013

LINKS

Reinhard Zumkeller, <a href="/A115068/b115068.txt">Table of n, a(n) for n = 1..7260</a>

STATUS

approved

editing

#5 by T. D. Noe at Sun Aug 07 16:13:08 EDT 2011

STATUS

proposed

approved

#4 by Clark Kimberling at Sun Aug 07 16:10:04 EDT 2011

STATUS

editing

proposed

#3 by Clark Kimberling at Sun Aug 07 16:10:00 EDT 2011

CROSSREFS

Cf. A007318, A038207, A193862.