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A072949
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Number of permutations p of (1,2,3,...,n) such that sum(k=1,n,abs(k-p(k)))=2n.
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2
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0, 0, 0, 4, 24, 148, 744, 3696, 17640, 83420, 390144, 1817652, 8438664, 39117852, 181136304, 838372452, 3879505944, 17952463180, 83086702848, 384626048292, 1781018204328
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Is a(n) always even?
More generally, T(n,k) (from A062869) appears to be even whenever k >= n. - Franklin T. Adams-Watters, Dec 11 2006. Max Alekseyev reports that both conjectures are true.
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MAPLE
| with(linalg): f := (i, j) -> x^(abs(i-j)):for n from 1 to 17 do A := matrix(n, n, f): printf("%d, ", coeff(permanent(A), x, 2*n)) od: - Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 27 2008
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PROG
| (PARI) a(n)=sum(k=1, n!, if(sum(i=1, n, abs(i-component(numtoperm(n, k), i)))-2*n, 0, 1))
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CROSSREFS
| Cf. A072948, A062869.
Sequence in context: A045915 A052609 A077613 * A104531 A045738 A192806
Adjacent sequences: A072946 A072947 A072948 * A072950 A072951 A072952
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KEYWORD
| more,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 20 2002
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EXTENSIONS
| More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 27 2008
a(18)-a(21) from Robert Gerbicz (robert.gerbicz(AT)gmail.com), Nov 21 2010
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