Permanents of m x n (0,1)-matrices with m and m-1 zeros
Jaap Spies
j.spies at hccnet.nl
Wed Nov 19 00:31:58 CET 2003
Jaap Spies wrote:
>
> y(m)=b(m,m+2)=(m+1)*y(m-1) + (m-1)*y(m-2), which is after a transformation:
>
> ID Number: A000153 (Formerly M1791 and N0706)
> URL: http://www.research.att.com/projects/OEIS?Anum=A000153
> Sequence: 0,1,2,7,32,181,1214,9403,82508,808393,8743994,103459471,
> 1328953592,18414450877,273749755382,4345634192131,
> 73362643649444,1312349454922513
> Name: a(n) = n*a(n-1) + (n-2)*a(n-2).
>
In general a column of Table I can be described with
y_d = (m-1+d)*y_d(m-1) + (m-1)*y_d(m-2)
The corresponding column of Tabel II can be calculated with
x_d = y_d(m-1) + y_d(m)
Indeed, we recognize A000255(n) = A000166(n-1) + A(000166(n)
and A055790(n) = A000255(n-1) + A000255(n).
A0????? = A000153(n-1) + A000153(n), etcetera.
From every a_old(n) we can make an a_new(n) = a_old(n-1) + a_old(n).
The question is, are those sequences interesting enough for submission
to the OEIS?
Jaap
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