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# Nexus Number

A nexus number is a figurate number built up of the nexus of cells less than steps away from a given cell. The th -dimensional nexus number is given by

 (1) (2)

where is a binomial coefficient. The symbolic representations and sequences for first few -dimensional nexus numbers are given in the table below.

 name 0 1 unit 1 odd number 2 hex number 3 rhombic dodecahedral number 4 nexus number
 OEIS , , , ... 0 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1 A005408 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ... 2 A003215 1, 7, 19, 37, 61, 91, 127, 169, 217, ... 3 A005917 1, 15, 65, 175, 369, 671, 1105, 1695, 2465, ... 4 A022521 1, 31, 211, 781, 2101, 4651, 9031, 15961, ...

Binomial Sums, Hex Number, Odd Number, Rhombic Dodecahedral Number

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## References

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 53-54, 1996.Sloane, N. J. A. Sequences A005408/M2400, A003215/M4362, A005917/M4968, and A022521 in "The On-Line Encyclopedia of Integer Sequences."

Nexus Number

## Cite this as:

Weisstein, Eric W. "Nexus Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NexusNumber.html