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A001883
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Number of permutations s of {1,2,...,n} such that |s(i)-i|>1 for each i=1,2,...,n.
(Formerly M3630 N1475)
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6
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1, 4, 29, 206, 1708, 15702, 159737, 1780696, 21599745, 283294740, 3995630216, 60312696452, 970234088153, 16571597074140, 299518677455165, 5711583170669554, 114601867572247060, 2413623459384988298
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,2
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COMMENTS
| Permanent of the (0,1)-matrix having (i,j)-th entry equal to 0 iff this is on the first lower-diagonal, diagonal or the first upper-diagonal. - Simone Severini (simoseve(AT)gmail.com), Oct 14 2004
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REFERENCES
| J. Riordan, ``The enumeration of permutations with three-ply staircase restrictions,'' unpublished memorandum, Bell Telephone Laboratories, Murray Hill, NJ, Oct 1963.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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PROG
| (PARI) permRWNb(a)=n=matsize(a)[1]; if(n==1, return(a[1, 1])); sg=1; in=vectorv(n); x=in; x=a[, n]-sum(j=1, n, a[, j])/2; p=prod(i=1, n, x[i]); for(k=1, 2^(n-1)-1, sg=-sg; j=valuation(k, 2)+1; z=1-2*in[j]; in[j]+=z; x+=z*a[, j]; p+=prod(i=1, n, x[i], sg)); return(2*(2*(n%2)-1)*p) for(n=1, 23, a=matrix(n, n, i, j, abs(i-j)>1); print1(permRWNb(a)", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), May 16 2007
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CROSSREFS
| Cf. A075851, A075852.
Sequence in context: A129587 A143551 A100022 * A135429 A079756 A087809
Adjacent sequences: A001880 A001881 A001882 * A001884 A001885 A001886
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms and better description from Reiner Martin (reinermartin(AT)hotmail.com), Oct 14 2002
More terms from Vladimir Baltic, Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 04 2003
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 16 2007
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