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A161720
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Half the difference between the first and the last numbers in the 7th circle of the cyclic representation of some structures whose cardinality generates Aminu numbers.
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0
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-1, 0, 2, 3, 5, 6, 8, 11, 12, 15, 17, 18, 20, 23, 26, 27, 30, 32, 33, 36, 38, 41, 45, 47, 48, 50, 51, 53, 60, 62, 65, 66, 71, 72, 75, 78, 80, 83, 86, 87, 92, 93, 95, 96, 102, 108, 110, 111, 113, 116, 117, 122, 125, 128, 131, 132
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,3
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COMMENTS
| A bijective operator is defined on the Aminu numbers which in turn generates another cyclic group. Aminu numbers were first reported as the cardinality of some subgroups of regular groups whose order and degree coincide, (Ibrahim,2004;2005;2007 and Ibrahim and Audu 2005).The action of the operator on the group structures where constructed using some special succession scheme which led to emergence of sequences such as A161719. This sequence enumerates half the difference between the first and last numbers in the 7th cycle of such group structures.
Is a(n)=A105760(n+1) ? [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 23 2009]
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REFERENCES
| A.A.Ibrahim,Group theoretic interpretation of Bara'a al-Dhimmah Models: Proceedings of Annual National Conference of Mathematical Association of Nigeria, MAN,(2004), 35-40.
A.AIbrahim and M.S.Audu, Some Group Theoretic Properties of Certain class of (123) and (132)- Avoiding Patterns of numbers: An enumeration scheme,African Journal of Natural Sciences, 8(1)(2005), 79-84.
A.A.Ibrahim, An Enumeration scheme and Algebraic properties of a special (132)- avoiding class of permutations Patterns, Trends in Applied sciences Research, Academic Journal Inc. 2(4)(2007), 334-340.
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FORMULA
| a(n)=(Pn-7)/2;Pn>=5
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EXAMPLE
| For Pn=5, a(1)=-2/2=-1, for Pn=7, a(2)=0/2=0, for Pn=11,a(3)=4/2=2
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PROG
| (Other) For Pn>=5 do the following let a(n)=(Pn-7)/2 write a(n) end.
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CROSSREFS
| Cf. A119626, A000040, A161719
Sequence in context: A138529 A035057 A005099 * A105760 A050834 A179799
Adjacent sequences: A161717 A161718 A161719 * A161721 A161722 A161723
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KEYWORD
| sign
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AUTHOR
| G. A. Isa (isaabor(AT)yahoo.com), Jun 18 2009
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