A374514 Number of n X n matrices whose values cover an initial interval of positive integers and whose rows and columns have values which are strictly increasing.
1, 1, 3, 197, 732963, 289599115433, 19454710000290140631, 324252739440855086589750626125, 1839663535877691613435674541258128354870051, 4664717625821787781559533555514908690826684467996898799881, 6714190347498763079980307954946450922919624466513063316268554904936722083543
Offset: 0
Keywords
Examples
The a(2) = 3 matrices are: [1 2] [1 2] [1 3] [2 3] [3 4] [2 4]
Links
- Ludovic Schwob, Table of n, a(n) for n = 0..20
- Andrew Howroyd, PARI Program, Sep 2024.
Crossrefs
Programs
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PARI
\\ See Links section for program file. vector(8, n, A374514(n-1))
Comments
Examples
For n=3 the three weak orderings are: 11<12=21<13=31=22<23=32<33, 11<12=21<22<13=31<23=32<33, and 11<12=21<13=31<22<23=32<33, which arise from the sets {1,2,3}, {1,2,4}, and {1,3,4}, respectively. For n=4, there are 39 weak orderings, but only 25 arise from sets of real numbers. For example, the weak ordering 11<12=21<13=31<22<14=41=23=32<24=42=33<34=43<44 does not arise from any set of real numbers.Links
Crossrefs
Formula
Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.
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