The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A135593 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A135593

Number of n X n symmetric (0,1)-matrices with exactly n+1 entries equal to 1 and no zero rows or columns.
(history; published version)

#14 by Jon E. Schoenfield at Fri Sep 18 04:14:53 EDT 2015

STATUS

editing

approved

#13 by Jon E. Schoenfield at Fri Sep 18 04:14:49 EDT 2015

FORMULA

Recurrence (for n>5): (n-5)*(n-2)*a(n) = (n-6)*n*a(n-1) + (n-4)*(n-1)*n*a(n-2) . - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 1/4*sqrt(2)*exp(sqrt(n)-n/2-1/4)*n^(n/2+3/2) . - Vaclav Kotesovec, Oct 20 2012

MAPLE

A135593 := proc(n) n!*coeftayl( x^2*(x+2)/2*exp(x*(x+2)/2), x=0, n) ; end: seq(A135593(n), n=2..40) ; - _# _R. J. Mathar_, Mar 31 2008

STATUS

approved

editing

#12 by Joerg Arndt at Sat May 25 10:02:22 EDT 2013

STATUS

proposed

approved

#11 by Vincenzo Librandi at Sat May 25 09:24:32 EDT 2013

STATUS

editing

proposed

#10 by Vincenzo Librandi at Sat May 25 09:24:25 EDT 2013

LINKS

Vincenzo Librandi, <a href="/A135593/b135593.txt">Table of n, a(n) for n = 2..200</a>

STATUS

approved

editing

#9 by Charles R Greathouse IV at Fri May 10 12:45:51 EDT 2013

AUTHOR

_Vladeta Jovovic (vladeta(AT)eunet.rs), _, Feb 25 2008

Discussion

Fri May 10

12:45

OEIS Server: https://oeis.org/edit/global/1911

#8 by Joerg Arndt at Sat Oct 20 07:00:35 EDT 2012

STATUS

editing

approved

#7 by Joerg Arndt at Sat Oct 20 07:00:24 EDT 2012

MATHEMATICA

Rest[Rest[CoefficientList[Series[x^2*(x+2)/2*E^(x*(x+2)/2), {x, 0, 20}], x]* Range[0, 20]!]] (* or _Vaclav Kotesovec_, Oct 20 2012 *)

STATUS

proposed

editing

#6 by Vaclav Kotesovec at Sat Oct 20 05:28:40 EDT 2012

STATUS

editing

proposed

#5 by Vaclav Kotesovec at Sat Oct 20 05:28:13 EDT 2012

FORMULA

Recurrence (for n>5): (n-5)*(n-2)*a(n) = (n-6)*n*a(n-1) + (n-4)*(n-1)*n*a(n-2) . - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 1/4*sqrt(2)*exp(sqrt(n)-n/2-1/4)*n^(n/2+3/2) . - Vaclav Kotesovec, Oct 20 2012

MATHEMATICA

Rest[Rest[CoefficientList[Series[x^2*(x+2)/2*E^(x*(x+2)/2), {x, 0, 20}], x]* Range[0, 20]!]] (* or *)

Flatten[{2, 9, RecurrenceTable[{(n-5)*(n-2)*a[n]==(n-6)*n*a[n-1]+(n-4)*(n-1)*n*a[n-2], a[4]==36, a[5]==140}, a, {n, 4, 20}]}] (* Vaclav Kotesovec, Oct 20 2012 *)

STATUS

approved

editing