A350293 -id:A350293 - cp's OEIS frontend

A350292 Triangle read by rows: the n-th row gives the saturated vertex Turán numbers for the cube graph Q_n.

1, 2, 1, 6, 3, 1, 12, 8, 4, 1, 24, 20, 10, 5, 1

Offset: 1

Stefano Spezia, Dec 23 2021

The k-th saturated vertex Turán number for the cube graph Q_n is the maximum number of vertices to be deleted from the cube graph such that no subgraph Q_k is complete and each of the deleted vertices being added again completes a subgraph Q_k (see Harborth and Nienborg).

			n\k |   1    2    3    4    5
----+------------------------
  1 |   1
  2 |   2    1
  3 |   6    3    1
  4 |  12    8    4    1
  5 |  24   20   10    5    1
  ...

Heiko Harborth and Hauke Nienborg, Saturated vertex Turán numbers for cube graphs, Congr. Num. 208 (2011), 183-188.
Mathonline, Cube Graphs

Cf. A350293 (k = 1), A350295 (2nd subdiagonal).

T(n, n) = 1 and T(n, n-1) = n (see Theorem 2 in Harborth and Nienborg).

A350294 a(n) = floor(n*2^n/(n + 1)).

Original entry on oeis.org

0, 1, 2, 6, 12, 26, 54, 112, 227, 460, 930, 1877, 3780, 7606, 15291, 30720, 61680, 123790, 248346, 498073, 998643, 2001826, 4011942, 8039082, 16106127, 32263876, 64623350, 129424237, 259179060, 518975214, 1039104990, 2080374784, 4164816771, 8337289456, 16689015778

Offset: 0

Stefano Spezia, Dec 23 2021

nonn

Robert Israel, Table of n, a(n) for n = 0..3305
Heiko Harborth and Hauke Nienborg, Saturated vertex Turán numbers for cube graphs, Congr. Num. 208 (2011), 183-188.
Mathonline, Cube Graphs

Cf. A000079, A350293.

f:= n -> floor(n*2^n/(n+1)):
map(f, [$0..40]); # Robert Israel, Dec 27 2021

Mathematica
```
Table[Floor[n 2^n/(n+1)],{n,0,34}]
```

A350293(n) <= a(n) (see Lemma 1 in Harborth and Nienborg).

a(n) ~ 2^n.

cp's OEIS Frontend

A350292 Triangle read by rows: the n-th row gives the saturated vertex Turán numbers for the cube graph Q_n.

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