decompwlj 3D

a(n) = (n^3 + 5*n + 18)/6

A060163 on the OEIS · family polynomial

Weight–level plate of a(n) = (n^3 + 5*n + 18)/6
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 viewerA060163 on the OEIS
Terms100,000 (n = -2 … 99,997)
Decomposable (a > 2d)99,992
Level class, k > L99,992 · 100.00 %
Weight class, k ≤ L0 · 0.00 %
Ties, k = L0
On the level line L = 15,352
Forced level, l ≤ d²99,991
Range of a(n)0 … 166,651,667,199,996
Range of the jump d1 … 4,999,750,004
Largest weight k, level L166,596,676,449,547, 33,114

99,998 different gaps occur, from 1 to 4,999,750,004; every decomposable term is forced level (l <= d^2); 8 terms do not decompose.

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.