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A160772
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Number of nodes (or order)of a graph model obtained using an automata scheme on sets of order Pn, Pn = n-th prime >=5 and in which all not halt sates are linked by arcs(edges).
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0
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13, 31, 91, 133, 240, 307, 463, 257, 871, 1261, 1561, 1723, 2071, 2451, 3081, 3307, 3541, 4291, 4831, 5113, 6007, 6643, 7657, 8011, 9121, 9901, 10303, 11131, 11991, 12433, 13341, 13807, 14281, 14763, 16771, 18361, 19586, 2117121757, 22351, 22953
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Special graph models were constructed (Ibrahim,2009) using an automata scheme invoving some tarnsition function defined on the Special (123)-avoiding permutation patterns reported by Ibrahim and Audu (2005; ibrahim,2008). The orde of these special variety of graph models represents an improvement of the earlier odels(Ibrahim 2008)in the study of the degree/diameter problems as used in circuit designs and analysis. The sequence represents the number of nodes(order) in this latest variety of graph models for primes Pn = 5,7,11,..., ie for Pn>=5.
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REFERENCES
| Ibrahim A.A. (2008) Some Transformation Schemes Involving the Special (132) - avoiding Permutation Patterns and a Binary Coding: An Algorithmic Approach Asian Journal of Algebra 1 (1):10-14, Asian Network for Scientific Information (ANSI), Pakistan
Ibrahim A.A and Audu M.S. (2005) Some Group theoretic Properties of Certain Class of (123) and (132)-Avoiding Patterns Numbers: an enumeration scheme African journal Natural Sciences Vol. 8: 79-84
Ibrahim A.A., and Audu M.S. (2008) On Stable Veriety of Cayley Graphs For Efficient Interconnection Networks Proceedings of Annual National Conference of Mathematical Association of Nigeria (MAN) held at Federal College of Education Technical, Gusau 26th- 30th August, 2008:156-161
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FORMULA
| T(Bn)= (Pn-2)(Pn-1)+1
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EXAMPLE
| For Pn = 5: T(Bn)= (3)(4)+1 = 13; for Pn = 7: T(Bn)= (5)(6)+1 =31
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PROG
| (Other) For Pn>=5 do the following Let T(Bn)= (Pn-2)(Pn-1)+1 Write T(Bn) end
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CROSSREFS
| Cf. A160771, A128929, A040976
Sequence in context: A158723 A107288 A095379 * A039403 A062339 A043226
Adjacent sequences: A160769 A160770 A160771 * A160773 A160774 A160775
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KEYWORD
| nonn,uned
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AUTHOR
| Aminu Alhaji Ibrahim (aminualhaji(AT)yahoo.co.uk), Jun 09 2009
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