trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Mathar's recurrence for A068551

The sequence a(n) = 4^n - binomial(2n, n), the total number of returns to the axis in all lattice paths with steps (1,1) and (1,-1) from the origin to (2n, 0), satisfies n a(n) + 2(3 - 4n) a(n - 1) + 8(2n - 3) a(n - 2) = 0 for every n at least 2, as conjectured by R. J. Mathar for OEIS A068551.

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Proof of the recurrence

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Mathar's recurrence for A068551Mathar's recurrence for A068551
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Lean sourceResearch workspace
Status
Closed
Depth
0
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/LatticeReturnsRecurrence
Repository path
D5/S3/Combinatorics/LatticeReturnsRecurrence.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
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b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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