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A062158
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n^3 - n^2 + n - 1.
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5
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-1, 0, 5, 20, 51, 104, 185, 300, 455, 656, 909, 1220, 1595, 2040, 2561, 3164, 3855, 4640, 5525, 6516, 7619, 8840, 10185, 11660, 13271, 15024, 16925, 18980, 21195, 23576, 26129, 28860, 31775, 34880, 38181, 41684, 45395, 49320, 53465, 57836, 62439, 67280, 72365, 77700, 83291, 89144, 95265, 101660
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(4) = 4^3-4^2+4-1 = 64-16+4-1 = 51
Number of walks of length 4 between any two distinct vertices of the complete graph K_{n+1} (n>=1). Example: a(2)=5 because in the complete graph ABC we have the following walks of length 4 between A and B: ABACB, ABCAB, ACACB,ACBAB and ACBCB. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,1000
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FORMULA
| a(n) = round[n^4/(n+1)] for n>2 = A062160(n, 4).
G.f.=(4x-1)(1+x^2)/(1-x)^4 (for the signed sequence). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
a(n) = floor(n^5/(n^2+n)), n>0 [From Gary Detlefs (gdetlefs(AT)aol.com), May 27 2010]
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MAPLE
| [seq(n^3-n^2+n-1, n=0..49)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 29 2006
a:=n->sum(1+sum(n, k=1..n), k=2..n):seq(a(n), n=0...43); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 24 2008]
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MATHEMATICA
| f[n_]:=n^3-n^2+n-1; f[Range[0, 60]] (*From Vladimir Joseph Stephan Orlovsky, Feb 05 2011*)
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PROG
| (PARI) { for (n=0, 1000, write("b062158.txt", n, " ", n*(n*(n - 1) + 1) - 1) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 02 2009]
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CROSSREFS
| Cf. A023443, A002061, A060884, A062159, A060888.
Sequence in context: A147488 A190094 A134481 * A034133 A006504 A007045
Adjacent sequences: A062155 A062156 A062157 * A062159 A062160 A062161
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KEYWORD
| easy,sign
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jun 08 2001
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
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