A128984 Degree of the special subgraph of Cayley graph constructed using the special (123)-avoiding and (132)-avoiding permutation patterns as generators.

2, 4, 6, 10, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 50, 52, 56, 58, 60, 66, 70, 72, 76, 78, 82, 86, 88, 90, 96, 100, 102, 106, 110, 112, 116, 118, 122, 128, 130, 136, 140, 142, 146, 148, 150, 156, 160, 166, 170, 172, 178, 180, 182, 186, 190, 192, 196, 198, 200, 202

Offset: 3

Author

Aminu Alhaji Ibrahim, Apr 30 2007

Keywords

• nonn
• uned

Comments

This sequence is constructed using a special veriety of subgraphs of Cayley graphs in order for a study of the degree/diameter problem.

References

• Ibrahim A.A. and Audu M.S.(2005) Some Group Theoretic Properties of Certain Class of (123) and (132)-Avoiding Patterns of Numbers: An Enumeration Scheme: An enumeration Scheme, African Journal of Natural Sciences, Vol. 8:79-84
• Ibrahim A.A. (2006) A Counting Scheme And Some Algebraic Properties of A Class of Special Permutation Patterns. (in preparation)
• Ibrahim A.A. (2005) On the Combinatorics of Succession In A 5-element Sample Abacus Journal of Mathematical Association of Nigeria Vol. 32, No. 2B:410-415

Crossrefs

Cf. A123642, A128929.

Formula

Recursion relation:f(0)=2, f(2)=4, f(3)=6, f(4)=12, f(5)=f(1)+f(2)+f(3)+f(4)/f(0), f(n)=f(n-1)+f(n-2)+f(n-3)+f(n-4)-f(n-5)/f(0)-f(n-5), n>5 and provided the difference between consecutive numbers (before and at the start of the addition) does not exceed four digits. If however, this difference (m-(m-1)<=4 the f(n)=f(n-1)+f(n-2)+f(n-3)+f(n-4)/f(0)-f(n-4). [Indices need to be changed to match the offset. - R. J. Mathar, Dec 04 2011]

Extensions

An obviously incorrect prime formula deleted. - R. J. Mathar, Dec 04 2011