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Date: 5-9-2020
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Date: 1-1-2021
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Date: 13-1-2021
793
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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
(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, ... |
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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