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, 82371572441063597524, 1880134860381149662936

Offset

1,1

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.

Formula

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

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

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

a(n) = 4 * (n-1)! * Sum_{k=0..n-1} (-1)^k * binomial(n+3-k, 4)/k!. - Sela Fried, Feb 11 2026

a(n) = 4 * A001909(n+2). - Alois P. Heinz, Feb 11 2026

Mathematica

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

Crossrefs

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

Sequence in context: A121146 A134006 A366434 * A333370 A125793 A121145

Adjacent sequences: A090010 A090011 A090012 * A090014 A090015 A090016

Keyword

nonn,easy

Author

Jaap Spies, Dec 13 2003

Extensions

Corrected by Jaap Spies, Jan 26 2004

Status

approved