A090014 Permanent of (0,1)-matrix of size n X (n+d) with d=4 and n-1 zeros not on a line.

5, 25, 155, 1135, 9545, 90445, 952175, 11016595, 138864365, 1893369505, 27756952355, 435287980375, 7269934161905, 128812336516885, 2413131201408695, 47652865538001595, 989254278781162325

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) = A001909(n-1) + A001909(n), a(1)=5

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

Programs

Mathematica

f[x_] := x*HypergeometricPFQ[{1, 5}, {}, x/(x+1)]/(x+1); Total /@ Partition[ CoefficientList[ Series[f[x], {x, 0, 18}], x], 2, 1] // Rest (* Jean-François Alcover, Nov 12 2013, after A001909 and Mark van Hoeij *)
t={5,25};Do[AppendTo[t,(n+3)*t[[-1]]+(n-2)*t[[-2]]],{n,3,17}];t (* Indranil Ghosh, Feb 21 2017 *)

Formula

a(n) = (n+3)*a(n-1) + (n-2)*a(n-2), a(1)=5, a(2)=25.

a(n) ~ exp(-1) * n! * n^4 / 24. - Vaclav Kotesovec, Nov 30 2017

Extensions

Corrected by Jaap Spies, Jan 26 2004