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Search: id:A062159
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| -1, 0, 21, 182, 819, 2604, 6665, 14706, 29127, 53144, 90909, 147630, 229691, 344772, 501969, 711914, 986895, 1340976, 1790117, 2352294, 3047619, 3898460, 4929561, 6168162, 7644119, 9390024, 11441325, 13836446, 16616907, 19827444, 23516129, 27734490, 32537631, 37984352, 44137269
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of walks of length 6 between any two distinct nodes of the complete graph K_{n+1} (n>=1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
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FORMULA
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a(n) = round[n^6/(n+1)] for n>2, = A062160(n,6).
G.f.=(76x^3+6x^2+27x^4+6x^5+6x-1)/(1-x)^6 (for the signed sequence). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
a(n) = (n^6-1)/(n+1). a(n) = (n-1)(n^2-n+1)(n^2+n+1) = (n-1)*A002061(n)*A002061(n+1). - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 12 2006
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EXAMPLE
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a(4) = 4^5-4^4+4^3-4^2+4-1 = 1024-256+64-16+4-1 = 819
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CROSSREFS
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Cf. A023443, A002061, A062158, A060884, A060888.
Cf. A002061.
Sequence in context: A113163 A090021 A025604 this_sequence A059721 A054370 A010827
Adjacent sequences: A062156 A062157 A062158 this_sequence A062160 A062161 A062162
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KEYWORD
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easy,sign
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jun 08 2001
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
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