StatisticalMechanics / CONCEPT
Mathar's recurrence for surviving walks from height 3
The number a(n) of walks s(0), ..., s(n) on the nonnegative integers with steps of size 1 and s(0) = 3 satisfies (n + 4)(n - 1) a(n) + (n - 1)(n + 1) a(n - 1) - 2(n + 1)(2n + 1) a(n - 2) - 4(n - 1)(n + 1) a(n - 3) = 0 for every n at least 3, as conjectured by R. J. Mathar for OEIS A026023. These walks are the paths of a random walker started at x = 4 that have not been adsorbed at x = 0 by time n.
Closed
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES1
PROOF DEPTH0
DOCUMENT LINKS1
Proof of the recurrence
RELATIONSHIP ATLAS
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Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
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Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Bounded Runs and Coherent Prefixesstructural-affinity · Closed
- Gelfondstructural-affinity · Closed
- Infinite Identification without Finite Exact Tomographystructural-affinity · Closed
- Mutual Abelian-Border Densities of Binary Word Pairsstructural-affinity · Closed
- Statistical Mechanics: Walk Countstructural-affinity · Closed
- Weighted Dyck Paths in a Stripstructural-affinity · Closed
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