A208976 Row sums of the triangle in A208101.

1, 2, 4, 8, 15, 29, 54, 104, 195, 377, 713, 1385, 2639, 5147, 9866, 19304, 37179, 72929, 140997, 277133, 537471, 1058147, 2057509, 4056233, 7904455, 15600899, 30458899, 60174899, 117675359, 232676279, 455657714, 901620584, 1767883499, 3500409329, 6871173869

Offset: 0

Author

Reinhard Zumkeller, Mar 04 2012

Keywords

• nonn

Comments

a(n) = A050168(n+1) - 1.

Number of Dyck (n+1)-paths that are symmetric after deleting all leading hills. - David Scambler, Aug 23 2012

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Programs

Haskell

a208976 n = a208976_list !! n
a208976_list = map (subtract 1) $ tail a050168_list

Mathematica

T[, 0] = 1; T[n, 1] := n; T[n_, n_] := T[n - 1, n - 2]; T[n_, k_] /; 1 < k < n := T[n, k] = T[n - 1, k] + T[n - 1, k - 2];
a[n_] := Sum[T[n, k], {k, 0, n}];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 03 2018, from A208101 *)

Formula

a(n) = A001405(n) + A001405(n+1) - 1.