cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Aminu Alhaji Ibrahim

Aminu Alhaji Ibrahim's wiki page.

Aminu Alhaji Ibrahim has authored 5 sequences.

A160772 Number of nodes (or order) of a graph model obtained using an automata scheme on sets of order prime(n) >= 5 and in which all not halt states are linked by arcs (edges).

Original entry on oeis.org

13, 31, 91, 133, 241, 307, 463, 757, 871, 1261, 1561, 1723, 2071, 2653, 3307, 3541, 4291, 4831, 5113, 6007, 6643, 7657, 9121, 9901, 10303, 11131, 11557, 12433, 15751, 16771, 18361, 18907, 21757, 22351, 24181, 26083, 27391, 29413, 31507, 32221, 35911, 36673
Offset: 3

Views

Author

Aminu Alhaji Ibrahim, Jun 09 2009

Keywords

Comments

Special graph models were constructed (Ibrahim, 2009) using an automata scheme involving some transition function defined on the Special (123)-avoiding permutation patterns reported by Ibrahim and Audu (2005; Ibrahim, 2008). The order of these special variety of graph models represents an improvement of the earlier models (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 >= 5.

Examples

			For prime(3) = 5: a(n) = (3)(4)+1 = 13; for prime(4) = 7: a(n) = (5)(6)+1 = 31

References

  • A. A. Ibrahim, 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 (2008).
  • A. A. Ibrahim and M. S. Audu, 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 (2005).
  • A. A. Ibrahim, and M. S. Audu, On Stable Variety 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 (2008).

Links

Crossrefs

Cf. A128929, A040976.

Programs

  • Magma
    [(NthPrime(n)-2)*(NthPrime(n)-1) + 1: n in [3..30]]; // G. C. Greubel, Apr 26 2018
  • Mathematica
    Table[(Prime[n] - 2) (Prime[n] - 1) + 1, {n, 3, 50}] (* T. D. Noe, Dec 30 2012 *)
  • PARI
    for(n=3, 50, print1((prime(n)-2)*(prime(n)-1) + 1, ", ")) \\ G. C. Greubel, Apr 26 2018

Formula

a(n) = (prime(n)-2)*(prime(n)-1) + 1.

Extensions

Terms changed by T. D. Noe, Dec 30 2012

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

Original entry on oeis.org

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

Views

Author

Aminu Alhaji Ibrahim, Apr 30 2007

Keywords

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

A128929 Diameter of a special type of regular graph of degree 4 whose order maintain an increase in form of an arithmetic progression.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21
Offset: 4

Views

Author

Aminu Alhaji Ibrahim, Apr 25 2007

Keywords

Examples

			f(D4,5)=1 when order=4, f(D4,5)=1 when order=5, f(D)=f(D4,5)+1=1+1=2 when order is 5+1=6

References

  • Claude C.S. and Dinneen M.J (1998), Group-theoretic methods for designing networks, Discrete mathematics and theoretical computer science, Research report
  • Comellas, F. and Gomez, J. (1995), New large graphs with given degree and diameter, in Proceedings of the seventh quadrennial international conference on the theory and applications of graphs, Volume 1: pp. 222-233
  • Ibrahim, A., A. (2007), A stable variety of Cayley graphs (in preparation)

Links

Crossrefs

Cf. A123642.
First differences of A186347.

Formula

f(D4,5)=1: Order =4,5; f(D)= f(D4,5)+n: order=5+n, n=1,2,...
I am assuming this sequence is just Floor[(n+5)/4]... [From Eric W. Weisstein, Sep 09 2008]

A123367 a(n) = (n! - 2^n)/8, n >= 4.

Original entry on oeis.org

1, 11, 82, 614, 5008, 45296, 453472, 4989344, 59874688, 778376576, 10897284352, 163459291904, 2615348727808, 44460928495616, 800296713183232, 15205637551038464, 304112751021948928, 6386367771463417856, 140500090972200435712, 3231502092360621031424
Offset: 4

Views

Author

Aminu Alhaji Ibrahim, Oct 12 2006

Keywords

Links

Crossrefs

Cf. A123642.

Programs

  • Magma
    [(Factorial(n)-2^n)/8: n in [4..25]]; // G. C. Greubel, Oct 13 2017
  • Mathematica
    Table[(n!-2^n)/8,{n,4,30}] (* Harvey P. Dale, Aug 19 2012 *)
  • PARI
    for(n=4,25, print1((n!-2^n)/8, ", ")) \\ G. C. Greubel, Oct 13 2017

Extensions

Corrected and extended by Harvey P. Dale, Aug 19 2012

A123642 a(n) = n! - 2^n.

Original entry on oeis.org

0, -1, -2, -2, 8, 88, 656, 4912, 40064, 362368, 3627776, 39914752, 478997504, 6227012608, 87178274816, 1307674335232, 20922789822464, 355687427964928, 6402373705465856, 121645100408307712, 2432902008175591424, 51090942171707342848, 1124000727777603485696
Offset: 0

Views

Author

Aminu Alhaji Ibrahim, Oct 04 2006

Keywords

Comments

Difference between the number of rows in the truth tables for circuit designs involving n variables and the order of S_n (the symmetric group on n symbols).

References

  • Audu, M. S. and Ibrahim, A. A., (2006) Discrete Mathematics With Applications (in preparation)
  • Ibrahim, A. A., (2006) A stable Variety of Cayley Graphs For Efficient Interconnection Networks (submitted)
  • Ibrahim, A. A. and Audu, M. S., (2005) Some Group theoretic Properties of Certain class of (123) and (132)-avoiding patterns of certain numbers; An enumeration Scheme. African Journal of Natural Sciences, Afri. J. Nat. Sci., 8: 79-84.

Links

Programs

  • Magma
    [Factorial(n)-2^n: n in [0..25]]; // G. C. Greubel, Oct 17 2017
  • Maple
    f:= gfun:-rectoproc({(-n+3)*a(n) +(n^2-n-4)*a(n-1) -2*(n-1)*(n-2)*a(n-2)=0,
a(0)=0, a(1)=-1, a(2)=-2, a(3)=-2}, a(n), remember): map(f, [$0..40]); # Georg Fischer, Mar 13 2020
  • Mathematica
    Table[n!-2^n,{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
  • PARI
    for(n=0,25, print1(n!-2^n, ", ")) \\ G. C. Greubel, Oct 17 2017
  • Sage
    [factorial(n)-2^n for n in range(0, 23)] # Zerinvary Lajos, Oct 27 2009

Formula

a(n) = A000142(n) - A000079(n). - Michel Marcus, Aug 12 2013
(-n+3)*a(n) +(n^2-n-4)*a(n-1) -2*(n-1)*(n-2)*a(n-2)=0 for n >= 3. - R. J. Mathar, Oct 20 2015; amended by Georg Fischer, Mar 13 2020
E.g.f.: 1/(1 - x) - exp(2*x). - G. C. Greubel, Oct 26 2017

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