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A058809
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The sequence lambda(3,n), where lambda is defined in A055203. Number of ways of placing n identifiable positive intervals with a total of exactly three starting and/or finishing points.
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5
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0, 0, 6, 24, 78, 240, 726, 2184, 6558, 19680, 59046, 177144, 531438, 1594320, 4782966, 14348904, 43046718, 129140160, 387420486, 1162261464, 3486784398, 10460353200, 31381059606, 94143178824, 282429536478, 847288609440
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| For all n, a(n)=1*3^n-3*1^n+3*0^n-1*0^n [with 0^0=1] where powers are taken of triangular numbers and multiplied by binomial coefficients with alternating signs.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| For n>0, a(n) = 3^n-3 = 3*a(n-1)+6.
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EXAMPLE
| a(2)=6 since intervals a-a and b-b can be combined as a-ab-b, a-b-ab, ab-a-b, b-ab-a, b-a-ab, or ab-b-a.
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CROSSREFS
| Cf. A059116, A059117.
Sequence in context: A080373 A180437 A162583 * A140088 A011855 A173031
Adjacent sequences: A058806 A058807 A058808 * A058810 A058811 A058812
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 03 2001
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EXTENSIONS
| Additional comments from Henry Bottomley, Jan 05 2001
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