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, ...

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."