A019266 Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for square lattice.

1, 0, 4, 12, 56, 280, 1488, 8232, 47008, 274824, 1636520, 9890584, 60510480, 374019776, 2332131872, 14651535840, 92653845120, 589317728376, 3767523372432, 24196006128592, 156030800105840, 1009911004804296, 6558631830442384, 42723991459518368, 279091277437885920

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..65

G. Thimm, Cycle sequences of crystal structures

G. Thimm and W. E. Klee, Zeolite cycle sequences, Zeolites, 19, pp. 422-424, 1997.

Formula

a(n) = A010566(n) / 2 = 2 * n * A002931(n) for n > 0. - Andrey Zabolotskiy, Jul 26 2022

Mathematica

(Length@FindCycle[{NearestNeighborGraph[Tuples[Range[2 # + 4], 2], {All, 1.}], {#+2, #+2}}, {2 #}, All]) &  /@ Range[11] (* Gabriel B. Apolinario, Jan 07 2017 *)

Crossrefs

Cf. A002931, A010566.

Sequence in context: A164575 A124004 A243785 * A009114 A144012 A197924

Adjacent sequences: A019263 A019264 A019265 * A019267 A019268 A019269

Keyword

nonn

Author

Georg Thimm (mgeorg(AT)ntu.edu.sg)

Extensions

a(11) from Gabriel B. Apolinario, Jan 07 2017

a(12)-a(18) from Aleksandr D. Krotov, Jan 07 2018

a(19)-a(20) from Aleksandr D. Krotov, Mar 22 2019

Terms a(21) and beyond added by Andrey Zabolotskiy, Jul 26 2022, using A002931

Status

approved