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A059116
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The sequence lambda(4,n), where lambda is defined in A055203. Number of ways of placing n identifiable positive intervals with a total of exactly four starting and/or finishing points.
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4
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0, 0, 6, 114, 978, 6810, 43746, 271194, 1653378, 9998970, 60229986, 362088474, 2174656578, 13054316730, 78345032226, 470127588954, 2820937720578, 16926142884090, 101558406986466, 609355090964634, 3656144492925378
(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*6^n-4*3^n+6*1^n-4*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) = 6^n-4*3^n+6.
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EXAMPLE
| a(2)=6 since intervals a-a and b-b can be combined as a-a-b-b, a-b-a-b, a-b-b-a, b-a-b-a, b-a-a-b, or b-a-a-b.
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PROG
| (MAGMA) [1*6^n-4*3^n+6*1^n-4*0^n+1*0^n: n in [0..30]]; // Vincenzo Librandi, Sep 23 2011
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CROSSREFS
| Cf. A058809, A059117.
Sequence in context: A051228 A194132 A194476 * A121544 A003425 A052465
Adjacent sequences: A059113 A059114 A059115 * A059117 A059118 A059119
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KEYWORD
| nonn,easy
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jan 05 2001
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