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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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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.
Sequence in context: A090366 A131965 A104982 this_sequence A052852 A121124 A087761
Adjacent sequences: A001906 A001907 A001908 this_sequence A001910 A001911 A001912
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KEYWORD
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nonn
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AUTHOR
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njas
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