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Date: 16-11-2020
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Date: 19-10-2019
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Date: 27-2-2020
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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
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(1) |
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(2) |
where is a binomial coefficient. The symbolic representations and sequences for first few
-dimensional nexus numbers are given in the table below.
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name |
0 | 1 | unit |
1 | ![]() |
odd number |
2 | ![]() |
hex number |
3 | ![]() |
rhombic dodecahedral number |
4 | ![]() |
nexus number |
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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, ... |
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."
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