A282198 - OEIS

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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, 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

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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

Table of n, a(n) for n=1..28.

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

Cf. A237593, A240542, A279286.

Sequence in context: A337476 A301876 A032026 * A158034 A002515 A096297

Adjacent sequences: A282195 A282196 A282197 * A282199 A282200 A282201

KEYWORD

nonn,more

AUTHOR

Hartmut F. W. Hoft, Feb 08 2017

STATUS

approved