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A300125
Number of closable Motzkin trees.
0
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
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
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Feb 25 2018
EXTENSIONS
More terms from Georg Fischer, Mar 29 2020
STATUS
approved