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Search: id:A001909
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| A001909 |
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a(n) = n*a(n-1) + (n-4)*a(n-2).
(Formerly M3576 N1450)
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+0
15
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| 0, 1, 4, 21, 134, 1001, 8544, 81901, 870274, 10146321, 128718044, 1764651461, 25992300894, 409295679481, 6860638482424, 121951698034461, 2291179503374234, 45361686034627361, 943892592746534964
(list; graph; listen)
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OFFSET
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2,3
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COMMENT
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With offset 1, permanent of (0,1)-matrix of size n X (n+d) with d=4 and n zeros not on a line. This is a special case of Theorem 2.3 of Seok-Zun Song et al. Extremes of permanents of (0,1)-matrices, p. 201-202. - Jaap Spies (j.spies(AT)hccnet.nl), Dec 12 2003
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
Brualdi, Richard A. and Ryser, Herbert J., Combinatorial Matrix Theory, Cambridge NY (1991), Chapter 7.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 188.
Seok-Zun Song et al., Extremes of permanents of (0,1)-matrices, Lin. Algebra and its Applic. 373 (2003), p. 197-210.
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FORMULA
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E.g.f.: exp(-x)/(1-x)^5 = sum_{n>=0} a(n+3)/n! x^n. - Michael Somos, Feb 19 2003
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PROGRAM
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(PARI) a(n)=if(n<2, 0, -contfracpnqn(matrix(2, n, i, j, j-4*(i==1)))[1, 1])
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CROSSREFS
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Cf. A000255, A000153, A000261, A001910, A090010, A055790, A090012-A090016.
Adjacent sequences: A001906 A001907 A001908 this_sequence A001910 A001911 A001912
Sequence in context: A090366 A131965 A104982 this_sequence A052852 A121124 A087761
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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