The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A121633

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A121633

Sum of the bottom levels of the last column over all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
(history; published version)

#13 by R. J. Mathar at Tue Jul 26 15:19:41 EDT 2022

STATUS

editing

approved

#12 by R. J. Mathar at Tue Jul 26 15:19:37 EDT 2022

FORMULA

D-finite with recurrence a(n) +(-2*n-1)*a(n-1) +(n^2+2*n-4)*a(n-2) +(-2*n^2+6*n-3)*a(n-3) +(n-3)^2*a(n-4)=0. - R. J. Mathar, Jul 26 2022

STATUS

approved

editing

#11 by Alois P. Heinz at Mon Sep 26 09:57:26 EDT 2016

STATUS

editing

approved

#10 by Alois P. Heinz at Mon Sep 26 09:57:22 EDT 2016

LINKS

Alois P. Heinz, <a href="/A121633/b121633.txt">Table of n, a(n) for n = 1..449</a>

#9 by Alois P. Heinz at Mon Sep 26 09:54:30 EDT 2016

DATA

0, 0, 1, 9, 68, 527, 4408, 40303, 403046, 4393339, 51955528, 663383135, 9102982354, 133668773755, 2092209897524, 34783032728383, 612234346270510, 11375905660965179, 222544581264066400, 4572536725690159999, 98456173247669999978, 2217126753620449439515

FORMULA

a(1)=0; a(n) =na n*a(n-1)+(n-1)!-1 for n>=2.

#8 by Alois P. Heinz at Mon Sep 26 09:53:21 EDT 2016

COMMENTS

a(n) = Sum(k*A121632(n,k), k>=0).

STATUS

approved

editing

#7 by Harvey P. Dale at Sun Dec 01 11:49:08 EST 2013

STATUS

editing

approved

#6 by Harvey P. Dale at Sun Dec 01 11:49:01 EST 2013

MATHEMATICA

RecurrenceTable[{a[1]==0, a[n]==n*a[n-1]+(n-1)!-1}, a, {n, 20}] (* Harvey P. Dale, Dec 01 2013 *)

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 18:53:56 EDT 2012

FORMULA

a(n)= A000254(n)- A002672(n) a(n)= n!*sum(1/k,k=1..10)- floor(n!(e-1)) [From _Gary Detlefs (gdetlefs(AT)aol.com), _, Jul 18 2010]

Discussion

Fri Mar 30

18:53

OEIS Server: https://oeis.org/edit/global/272

#4 by Russ Cox at Fri Mar 30 17:36:10 EDT 2012

AUTHOR

_Emeric Deutsch (deutsch(AT)duke.poly.edu), _, Aug 12 2006

Discussion

Fri Mar 30

17:36

OEIS Server: https://oeis.org/edit/global/173