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Nexus Number


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

N_d(n)=sum_(k=0)^(d)(d+1; k)n^k
(1)
=(n+1)^(d+1)-n^(d+1),
(2)

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

dOEISN_d(0), N_d(1), N_d(2), ...
01, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1A0054081, 3, 5, 7, 9, 11, 13, 15, 17, 19, ...
2A0032151, 7, 19, 37, 61, 91, 127, 169, 217, ...
3A0059171, 15, 65, 175, 369, 671, 1105, 1695, 2465, ...
4A0225211, 31, 211, 781, 2101, 4651, 9031, 15961, ...

See also

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."

Referenced on Wolfram|Alpha

Nexus Number

Cite this as:

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

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