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%I #22 Mar 19 2021 07:02:20
%S 3,9,39,213,1395,10617,91911,890901,9552387,112203465,1432413063,
%T 19743404469,292164206259,4619383947513,77708277841575,
%U 1385712098571957,26108441941918851,518231790473609481,10808479322484810087
%N Permanent of (0,1)-matrix of size n X (n+d) with d=2 and n-1 zeros not on a line.
%D Brualdi, Richard A. and Ryser, Herbert J., Combinatorial Matrix Theory, Cambridge NY (1991), Chapter 7.
%H Indranil Ghosh, <a href="/A090012/b090012.txt">Table of n, a(n) for n = 1..447</a>
%H Seok-Zun Song et al., <a href="https://doi.org/10.1016/S0024-3795(03)00382-3">Extremes of permanents of (0,1)-matrices</a>, Lin. Algebra and its Applic. 373 (2003), pp. 197-210.
%F a(n) = (n+1)*a(n-1) + (n-2)*a(n-2), a(1)=3, a(2)=9.
%F a(n) = A000153(n-1) + A000153(n), a(1)=3.
%F G.f.: W(0)/x -1/x, where W(k) = 1 - x*(k+3)/( x*(k+2) - 1/(1 - x*(k+1)/( x*(k+1) - 1/W(k+1) ))); (continued fraction). - _Sergei N. Gladkovskii_, Aug 25 2013
%F a(n) ~ exp(-1) * n! * n^2 / 2. - _Vaclav Kotesovec_, Nov 30 2017
%p A090012 := proc(n,d) local r; if (n=1) then r := d+1 elif (n=2) then r := (d+1)^2 else r := (n+d-1)*A090012(n-1,d)+(n-2)*A090012(n-2,d) fi; RETURN(r); end: seq(A090012(n,2),n=1..20);
%t t={3,9};Do[AppendTo[t,(n+1)*t[[-1]]+(n-2)*t[[-2]]],{n,3,19}];t (* _Indranil Ghosh_, Feb 21 2017 *)
%t RecurrenceTable[{a[1]==3,a[2]==9,a[n]==(n+1)a[n-1]+(n-2)a[n-2]},a,{n,20}] (* _Harvey P. Dale_, Sep 21 2017 *)
%o (Python)
%o # Program to generate the b-file
%o print("1 3")
%o print("2 9")
%o a=3
%o b=9
%o c=(3+1)*b+(3-2)*a
%o for i in range(4, 40):
%o print(str(i - 1)+" "+str(c))
%o a=b
%o b=c
%o c=(i+1)*b+(i-2)*a # _Indranil Ghosh_, Feb 21 2017
%Y Cf. A000255, A000153, A000261, A001909, A001910, A090010, A055790, A090013-A090016.
%K nonn,easy
%O 1,1
%A _Jaap Spies_, Dec 13 2003
%E Corrected by _Jaap Spies_, Jan 26 2004
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