bibkey: mathar2016a270236 authors: R. J. Mathar year: 2016 title: “OEIS A270236, Triangle T(n,p): occurrences of p in the restricted growth functions of length n” doi: null url: https://oeis.org/A270236 claim: “NAME (R. J. Mathar, 2016-03-13): Triangle T(n,p) read by rows: the number of occurrences of p in the restricted growth functions of length n. COMMENT (R. J. Mathar, 2016-03-13): The RG functions used here are defined by f(1)=1, f(j) <= 1+max_{i<j} f(i). FORMULA (R. J. Mathar, 2016-03-13): Conjecture: T(n,n-1) = 2+n*(n-1)/2 for n>1. FORMULA (R. J. Mathar, 2016-03-13; index correction Alois P. Heinz, 2016-03-18): Conjecture: T(n+1,n-1) = 2+n*(n+1)(3n^2-5*n+26)/24 for n>1.” strata_touched:

• D5/S1/Recurrence/Invariants/RestrictedGrowthLabelOccurrences license: citation-only triage: anchor

OEIS A270236

R. J. Mathar’s entry counts occurrences of labels across restricted growth functions. The functions begin with label 1, and each later label is at most one greater than the maximum earlier label. The two formulas below were entered as conjectures on March 13, 2016. Alois P. Heinz corrected the left index of the second formula on March 18, 2016.

The formal model stores each restricted growth function in reverse chronological order. Its recursive extension rule is equivalent to the displayed forward definition, and its statistic sums List.count p over all words of the requested length. Both divisions in the closed forms are natural-number quotients.

Verified locator

• URL: https://oeis.org/A270236
• Locator: NAME; COMMENTS, R. J. Mathar, Mar 13 2016; FORMULA, R. J. Mathar, Mar 13 2016; revision #22, Alois P. Heinz, Mar 18 2016.

Triangle T(n,p) read by rows: the number of occurrences of p in the restricted growth functions of length n.

The RG functions used here are defined by f(1)=1, f(j) <= 1+max_{i<j} f(i).

Conjecture: T(n,n-1) = 2+n*(n-1)/2 for n>1.

Conjecture: T(n+1,n-1) = 2+n*(n+1)(3n^2-5*n+26)/24 for n>1.