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 | = | (n + 1)^(d + 1) - n^(d + 1), 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.

binomial sums | hex number | odd number | rhombic dodecahedral number