A294490 Triangle read by rows: T(n,k) is the number of connected graphs on n vertices having independence number k.

1, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 11, 8, 1, 0, 1, 34, 63, 13, 1, 0, 1, 103, 524, 205, 19, 1, 0, 1, 405, 5863, 4308, 513, 26, 1, 0, 1, 1892, 100702, 135563, 21782, 1105, 34, 1, 0, 1, 12166, 2880002, 7161399, 1576634, 84185, 2140, 43, 1, 0, 1, 105065, 138772607, 652024627, 203380116, 12140094, 274156, 3845, 53, 1, 0

Offset

1,8

Comments

Bivariate inverse Euler transform of A263341. This sequence can be derived from A263341 because the independence number of a disconnected graph is the sum of the independence numbers of its components. - Andrew Howroyd, Feb 19 2020

Links

Andrew Howroyd, Table of n, a(n) for n = 1..91 (first 13 rows derived from Brendan McKay data in A263341)

Example

Triangle begins:
  1;
  1,   0;
  1,   1,    0;
  1,   4,    1,    0;
  1,  11,    8,    1,   0;
  1,  34,   63,   13,   1,  0;
  1, 103,  524,  205,  19,  1, 0;
  1, 405, 5863, 4308, 513, 26, 1, 0;
  ...

Crossrefs

Columns 2..5 are A243781, A243782, A243783, A243784.

Row sums give A001349.

Cf. A263341 (not necessarily connected).

Sequence in context: A343648 A359363 A318996 * A085852 A123125 A173018

Adjacent sequences: A294487 A294488 A294489 * A294491 A294492 A294493

Keyword

nonn,tabl

Author

Andrew Howroyd, Oct 31 2017

Extensions

Terms a(56) and beyond derived from A263341 added by Andrew Howroyd, Feb 19 2020

Status

approved