A090015 Permanent of (0,1)-matrix of size n X (n+d) with d=5 and n-1 zeros not on a line.

6, 36, 258, 2136, 19998, 208524, 2393754, 29976192, 406446774, 5930064372, 92608986546, 1541044428456, 27216454135758, 508388707585116, 10013199347882058, 207381428863832784, 4505207996358719334

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..445
• 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) = A001910(n-1) + A001910(n), a(1)=6

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

Programs

Maple

f:= gfun:-rectoproc({a(n) = (n+4)*a(n-1) + (n-2)*a(n-2),a(1)=6,a(2)=36},a(n),remember):
map(f, [$1..40]); # Robert Israel, Nov 26 2018

Mathematica

t={6,36};Do[AppendTo[t,(n+4)*t[[-1]]+(n-2)*t[[-2]]],{n,3,17}];t (* Indranil Ghosh, Feb 21 2017 *)
RecurrenceTable[{a[n] == (n+4)*a[n-1] + (n-2)*a[n-2],
a[1] == 6, a[2] == 36}, a, {n, 1, 40}] (* Jean-François Alcover, Sep 16 2022, after Robert Israel *)

Formula

a(n) = (n+4)*a(n-1) + (n-2)*a(n-2), a(1)=6, a(2)=36

a(n) ~ exp(-1) * n! * n^5 / 5!. - Vaclav Kotesovec, Nov 30 2017

a(n) = ((n^6+21*n^5+160*n^4+545*n^3+814*n^2+415*n+1)*exp(-1)*Gamma(n, -1)+(-1)^n*(n^5+20*n^4+141*n^3+422*n^2+499*n+154))/120. - Robert Israel, Nov 26 2018

Extensions

Corrected by Jaap Spies, Jan 26 2004