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

[Brendan McKay]

It continues 1775935516860530625139, 230933325874558862792569

and I started A352258.

Richard, I didn't understand the relevance of Erdos-Kleitman so
I didn't cite it, but feel free to add that.

Brendan.

On 9/3/2022 9:42 pm, Brendan McKay via SeqFan wrote:
> 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%7Cea639fa29fa94c7405d408da01b98cb5%7Ce37d725cab5c46249ae5f0533e486437%7C0%7C0%7C637824194147808535%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=G9X%2Fzi%2BwfxNVYdiYAefYT%2F4CvptsnFPXjWcqqFUWhUs%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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