Metadata
bibkey: schulte2017a060693
authors: Werner Schulte
year: 2017
title: "OEIS A060693, Triangle read by rows: T(n, k) is the number of Schröder paths from (0,0) to (2n,0) having k peaks"
doi: null
url: https://oeis.org/A060693
claim: "Triangle (0 <= k <= n) read by rows: T(n, k) is the number of Schröder paths from (0,0) to (2n,0) having k peaks. T(n,k) is the number of Schroeder paths (i.e., consisting of steps U=(1,1), D=(1,-1), H=(2,0) and never going below the x-axis) from (0,0) to (2n,0), having k peaks. Example: T(2,1)=3 because we have UU*DD, U*DH and HU*D, the peaks being shown by *. Conjecture: Sum_{k=0..n} (-1)^k*T(n,k)*(n+1-k)^2 = 1+n+n^2. - _Werner Schulte_, Jan 11 2017"
strata_touched:
- D5/S1/Recurrence/Invariants/SchroederPeakAlternatingQuadraticMoment
license: citation-only
triage: anchor
OEIS A060693
The entry’s name, comment, and formula fields provide the path definition and Schulte’s alternating quadratic-moment conjecture. The formalization uses the same U, D, H steps, endpoint, nonnegativity condition, and adjacent U,D peak statistic.
Verified locator
- URL: https://oeis.org/A060693
- Locator: NAME and COMMENTS, Emeric Deutsch, Dec 06 2003; FORMULA, Werner Schulte, Jan 11 2017.
The FORMULA conjecture line is:
Conjecture: Sum_{k=0..n} (-1)^kT(n,k)(n+1-k)^2 = 1+n+n^2. - Werner Schulte, Jan 11 2017