A090016 Permanent of (0,1)-matrix of size n X (n+d) with d=6 and n-1 zeros not on a line.

7, 49, 399, 3689, 38087, 433713, 5394991, 72737161, 1056085191, 16423175153, 272275569167, 4792916427369, 89267526953479, 1753598009244529, 36232438035285807, 785431570870425353, 17822981129678644871

Offset: 1

Author

Jaap Spies, Dec 13 2003

Keywords

• nonn
• easy

References

• Brualdi, Richard A. and Ryser, Herbert J., Combinatorial Matrix Theory, Cambridge NY (1991), Chapter 7.

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..444
• Seok-Zun Song et al., Extremes of permanents of (0,1)-matrices, Lin. Algebra and its Applic. 373 (2003), pp. 197-210.

Crossrefs

a(n) = A090010(n-1) + A090010(n), a(1)=7

Cf. A000255, A000153, A000261, A001909, A001910, A090010, A055790, A090012-A090015.

Programs

Mathematica

t={7,49};Do[AppendTo[t,(n+5)*t[[-1]]+(n-2)*t[[-2]]],{n,3,17}];t (* Indranil Ghosh, Feb 21 2017 *)

Formula

a(n) = (n+5)*a(n-1) + (n-2)*a(n-2), a(1)=7, a(2)=49

E.g.f.: 7*exp(-x)/(1-x)^8. - Vladeta Jovovic, Mar 19 2004

a(n) = (A000166(n-1)+7*A000166(n)+21*A000166(n+1)+35*A000166(n+2)+35*A000166(n+3)+21*A000166(n+4)+7*A000166(n+5)+A000166(n+6))/6!. - Vladeta Jovovic, Mar 19 2004

a(n) ~ exp(-1) * n! * n^6 / 6!. - Vaclav Kotesovec, Nov 30 2017

Extensions

Corrected by Jaap Spies, Jan 26 2004