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Search: id:A006458
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| A006458 |
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Number of elements in Z[ omega ] whose `smallest algorithm' is <= n, where omega = -omega+1.
(Formerly M4399)
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+0
3
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| 1, 7, 31, 115, 391, 1267, 3979, 12271, 37423, 113371, 342091, 1029799, 3095671, 9298147, 27914179, 83777503, 251394415, 754292827, 2263072411, 6789560407
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
P. Samuel, About Euclidean rings, J. Alg., 19 (1971), 282-301.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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a(n+6)-5a(n+5)+5a(n+4)+5a(n+3)-4a(n+2)-8a(n+1)+6a(n)=0.
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MAPLE
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A006458:=(1+2*z+z**2+2*z**4+6*z**5)/(3*z-1)/(2*z**3+2*z**2-1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Cf. A006457, A006459.
Adjacent sequences: A006455 A006456 A006457 this_sequence A006459 A006460 A006461
Sequence in context: A109756 A055580 A097786 this_sequence A091344 A032197 A114289
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KEYWORD
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nonn,easy,nice
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AUTHOR
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H. W. Lenstra, Jr.
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 08 2006
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