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

Offset: 1

Author

Hartmut F. W. Hoft, Feb 08 2017

Keywords

• nonn
• more

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.

Examples

			a(4) = 23 since the point on the diagonal is A279286(4) = 15 and only A240542(20)..A240542(23) = 15.
		

Crossrefs

Cf. A237593, A240542, A279286.

Programs

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]]
				

Formula

a(n) = max( k : A279286(n) = A240542(k) ), for n >= 1.