A300125 Number of closable Motzkin trees.

0, 1, 1, 2, 5, 11, 26, 65, 163, 417, 1086, 2858, 7599, 20391, 55127, 150028, 410719, 1130245, 3124770, 8675210, 24175809, 67603633, 189633981, 533463183, 1504644945, 4254179693, 12055097308, 34231674486, 97392368007, 277590288931, 792528581088

Offset

0,4

Comments

From the Bodini-Tarau paper: a closable Motzkin tree is "the skeleton of at least one closed lambda term".

Links

Table of n, a(n) for n=0..30.

Olivier Bodini, Paul Tarau, On Uniquely Closable and Uniquely Typable Skeletons of Lambda Terms, arXiv:1709.04302 [cs.PL], 2017.

Maple

f:= gfun:-rectoproc({
  (384*n^2 +384*n)        *a(n  ) +
  (-32*n^2-512*n-480)     *a(n+1) +
  (-368*n^2 -2192*n-2928) *a(n+2) +
  (-56*n^2 -344*n-504)    *a(n+3) +
  (-4*n^2 +188*n+852)     *a(n+4) +
  (110*n^2 +1034*n+2328)  *a(n+5) +
  (-21*n^2 -201*n-390)    *a(n+6) +
  (-21*n^2 -327*n-1272)   *a(n+7) +
  (9*n^2 +153*n+648)      *a(n+8) +
  (-n^2 -19*n-90)         *a(n+9) = 0,
  a(0) = 0, a(1) = 0, a(2) = 1, a(3) = 1, a(4) = 2, a(5) = 5, a(6) = 11, a(7) = 26, a(8) = 65
}, a(n), remember): map(f, [$1..64]); # Georg Fischer, Mar 29 2020 (from the Bodini-Tarau paper)

Crossrefs

Cf. A000108, A001006, A135501.

Sequence in context: A308060 A235496 A025245 * A307576 A079223 A095892

Adjacent sequences: A300122 A300123 A300124 * A300126 A300127 A300128

Keyword

nonn

Author

Michael De Vlieger, Feb 25 2018

Extensions

More terms from Georg Fischer, Mar 29 2020

Status

approved