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

Author

Michael De Vlieger, Feb 25 2018

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A000108, A001006, A135501.

Programs

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)

Extensions

More terms from Georg Fischer, Mar 29 2020