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Search: id:A071798
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| A071798 |
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Number of paths on the surface of the n-dimensional lattice [0..2]^n; i.e. the lattice paths that do not pass through the point (1,1,...,1). |
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+0
1
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| 0, 2, 54, 1944, 99000, 6966000, 655678800, 80103945600, 12372954249600, 2362712677920000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(2) + 1 = 3 is prime. a(3) - 1 = 53 is prime. a(5) - 1 = 98999 is prime. a(7) + 1 = 655678801 is prime. a(8) - 1 = 80103945599 is prime, and part of a twin prime, as a(8) + 1 = 80103945601 is prime. a(13) - 1 = 49191138900262719359999 is prime. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 01 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..50
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n)=(2n)!/2^n-(n!)^2
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MATHEMATICA
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Table[(2n)!/2^n-(n!)^2, {n, 10}]
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CROSSREFS
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Cf. A000680.
Sequence in context: A055024 A057411 A157058 this_sequence A123686 A122418 A069788
Adjacent sequences: A071795 A071796 A071797 this_sequence A071799 A071800 A071801
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KEYWORD
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easy,nice,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jun 06 2002
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EXTENSIONS
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Situations in which a(n) -1 or a(n)+1 are primes for n = 1..30. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 01 2009]
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