A286513 Array read by antidiagonals: T(m,n) = number of independent sets in the cylinder graph C_m X P_n.

1, 1, 3, 1, 7, 4, 1, 17, 13, 7, 1, 41, 43, 35, 11, 1, 99, 142, 181, 81, 18, 1, 239, 469, 933, 621, 199, 29, 1, 577, 1549, 4811, 4741, 2309, 477, 47, 1, 1393, 5116, 24807, 36211, 26660, 8303, 1155, 76, 1, 3363, 16897, 127913, 276561, 307983, 143697, 30277, 2785, 123

Offset

1,3

Comments

Equivalently, the number of vertex covers in the cylinder graph C_m X P_n.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..435

Eric Weisstein's World of Mathematics, Independent Vertex Set

Wikipedia, Independent set

Example

Table starts:
=============================================================
m\n|   1    2     3      4        5         6           7
---|---------------------------------------------------------
1  |   1    1     1      1        1         1           1 ...
2  |   3    7    17     41       99       239         577 ...
3  |   4   13    43    142      469      1549        5116 ...
4  |   7   35   181    933     4811     24807      127913 ...
5  |  11   81   621   4741    36211    276561     2112241 ...
6  |  18  199  2309  26660   307983   3557711    41097664 ...
7  |  29  477  8303 143697  2488431  43089985   746156517 ...
8  |  47 1155 30277 788453 20546803 535404487 13951571713 ...
...

Crossrefs

Rows 3-8 are A003688(n+1), A051926, A181989, A181961, A182014, A182019.

Columns 1-4 are A000032, A051927, A050400, A050401.

Main diagonal is A212270.

Cf. A089934 (P_m X P_n), A027683, A286514.

Sequence in context: A275599 A210038 A319076 * A193970 A274510 A158841

Adjacent sequences: A286510 A286511 A286512 * A286514 A286515 A286516

Keyword

nonn,tabl

Author

Andrew Howroyd, May 10 2017

Status

approved