[seqfan] Re: Max no. of edges in graph with no 4-cycles

[Brendan McKay]

I agree with these and have continuation

  5774524092,  376068483351, 31643635513816, 3401292647423655,
  462391295351625128, 78801283167350942685

I'll add the sequence when one more finishes.

Brendan.

On 9/3/2022 3:26 am, Richard J. Mathar wrote:
> Related to A006855 I stumbled across the Erd"os-Kleitman paper
> https://aus01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdoi.org%2F10.1090%2FS0002-9939-1971-0270924-9&data=04%7C01%7Cbrendan.mckay%40anu.edu.au%7C9bd607f555194f23785708da01207c5c%7Ce37d725cab5c46249ae5f0533e486437%7C0%7C0%7C637823984149038033%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=Sjpy67ZBU6WFPoT8Y4X7Zq0tdeR0SrwPRqybawqYxwA%3D&reserved=0
> "On collections of subsets containing no 4-member boolean algebra"
> Proc. Am. Math. Soc. 28 (1) (1971) page 87
> I'm trying to count the number of symmetric binary (with entries of {0,1})
> nXn matrices which have no 2x2 submatrix with all 4 entries =1.
> For n=1,2,3,.. I get
> 2,
> 7,
> 42,
> 399,
> 5614
> 112221
> 3102020
> 116076057
> which is not in the OEIS. Can anyone confirm these (and submit
> the known terms)?
> If the requirement on the 2x2 submatrices is dropped, all
> symmetric binary matrices are counted, which is 2^(n*(n+1)/2)),
> because there are n*(n+1)/2 independent elements in the (upper or lower)
> triangular submatrix.
>
> See perhaps also A350296, A350304.
> This is also weakly related to A350237
>
> Best regards, Richard Mathar
>
> --
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