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A282198 a(n) = k if the last Dyck path that is counted in A279286(n) is the k-th Dyck path. 1
1, 3, 11, 23, 76, 149, 431, 539, 659, 1343, 2678, 2939, 6524, 6929, 8414, 8873, 10027, 25367, 27299, 87073, 113071, 122875, 178595, 185534, 599237, 1308195, 1888172, 4803699 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Since there are 19 concurrent Dyck paths through diagonal position 19818 (not in A279286) that occur after 20 concurrent Dyck paths at position 18915 (in A279286), number 28594 does not occur in this sequence while 27299 does.
For more information about the Dyck paths mentioned see A237593.
LINKS
FORMULA
a(n) = max( k : A279286(n) = A240542(k) ), for n >= 1.
EXAMPLE
a(4) = 23 since the point on the diagonal is A279286(4) = 15 and only A240542(20)..A240542(23) = 15.
MATHEMATICA
a240542[n_] := Sum[(-1)^(k+1)*Ceiling[(n+1)/k - (k+1)/2], {k, 1, Floor[(Sqrt[8n+1]-1)/2]}]
a282198[b_] := Module[{centers={{1, 1}}, acc={1}, k=2, cPrev=1, cCur, len}, While[k<=b, cCur=a240542[k]; If[Last[acc]==cCur, AppendTo[acc, cCur], len=Length[acc]; If[First[Last[centers]]<len, AppendTo[centers, {len, k-1}]]; acc={cCur}; cPrev=cCur]; k++]; Last[Transpose[centers]]]
a282198[5000000] (* data *)
CROSSREFS
Sequence in context: A337476 A301876 A032026 * A158034 A002515 A096297
KEYWORD
nonn,more
AUTHOR
Hartmut F. W. Hoft, Feb 08 2017
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)