A090013 Permanent of (0,1)-matrix of size n X (n+d) with d=3 and n-1 zeros not on a line.

4, 16, 84, 536, 4004, 34176, 327604, 3481096, 40585284, 514872176, 7058605844, 103969203576, 1637182717924, 27442553929696, 487806792137844, 9164718013496936, 181446744138509444, 3775570370986139856

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..446
• 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) = A000261(n-1) + A000261(n), a(1)=4

Cf. A000255, A000153, A000261, A001909, A001910, A090010, A055790, A090012-A090016.

Programs

Mathematica

t={4,16};Do[AppendTo[t,(n+2)*t[[-1]]+(n-2)*t[[-2]]],{n,3,18}];t (* Indranil Ghosh, Feb 21 2017 *)

Formula

a(n) = (n+2)*a(n-1) + (n-2)*a(n-2), a(1)=4, a(2)=16

a(n) ~ exp(-1) * n! * n^3 / 6. - Vaclav Kotesovec, Nov 30 2017

Extensions

Corrected by Jaap Spies, Jan 26 2004