A112850 Number of graph endomorphisms of undirected cycles of even length: |End(C_2n)|.

2, 32, 132, 576, 2540, 11112, 48076, 205952, 875196, 3695160, 15519548, 64899792, 270415652, 1123264856, 4653525660, 19234572544, 79342611548, 326704870872, 1343120024476, 5513861152880, 22606830726564, 92580354403768, 378737813469692, 1547884976788896, 6320530321887700, 25787763713301512

Offset: 1

Author

Martin Alexander Michels (martinmichels(AT)t-online.de), Sep 24 2005

Keywords

• easy
• nonn

References

• M. A. Michels, About The Structure of Graph Endomorphisms, Diploma thesis, University of Oldenburg, Germany, 2005

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• M. A. Michels and U. Knauer, The congruence classes of paths and cycles, Discrete Math., 309 (2009), 5352-5359. [_N. J. A. Sloane_, Sep 15 2009]

Crossrefs

Cf. A112849.

Programs

Magma

[2] cat [2*n*(2 + Binomial(2*n-1, n-1) + Binomial(2*n-1, n)): n in [2..30]]; // Vincenzo Librandi, Nov 21 2018

Mathematica

Join[{2}, Table[2 n (2 + Binomial[2 n - 1, n - 1] + Binomial[2 n - 1, n]), {n, 2, 25}]] (* Vincenzo Librandi, Nov 21 2018 *)

Formula

|End(C_2n)| = 2n*(2 + binomial(2n-1, n-1) + binomial(2n-1, n)) for n > 1.

Extensions

Corrected first term from 4 to 2 and added "n > 1" in the formula, which is not correct when n=1. - James D. Mitchell (jdm3(AT)st-and.ac.uk), Sep 21 2010