Number of points on surface of cuboctahedron (or icosahedron): a(0) = 1; for n > 0, a(n) = 10n^2 + 2. Also coordination sequence for f.c.c. or A_3 or D_3 lattice

Weight–level plate of Number of points on surface of cuboctahedron (or icosahedron): a(0) = 1; for n > 0, a(n) = 10n^2 + 2. Also coordination sequence for f.c.c. or A_3 or D_3 lattice — Click the plate to explore it in 3-D. Weight k across, level L up, both on log scales: blue in the weight class (k ≤ L), orange in the level class (k > L). The dashed diagonal is k = L.

Open in the 3-D viewer A005901 on the OEIS

Terms	100,000 (n = 0 … 99,999)
Decomposable (a > 2d)	99,995
Level class, k > L	99,995 · 100.00 %
Weight class, k ≤ L	0 · 0.00 %
Ties, k = L	0
On the level line L = 1	2
Forced level, l ≤ d²	99,995
Range of a(n)	1 … 99,998,000,012
Range of the jump d	11 … 1,999,990
Largest weight k, level L	49,986,000,971, 49,704

Every gap is different, from 11 to 1,999,990; every decomposable term is forced level (l <= d^2).

The decomposition

Every term of a strictly increasing sequence is written a(n) = k(n)·L(n) + d(n): the jump d = a(n+1) − a(n), the weight k the least divisor of a − d greater than d, the level L = (a − d)/k. A term decomposes when a > 2d; it is in the level class when k > L and in the weight class when k ≤ L. See decompwlj.com and arXiv:0711.0865, or how it works, with worked examples and a live one.