A369360 a(n) is the number of interior points over all Motzkin polyominoes of length n.

1, 6, 25, 93, 324, 1088, 3565, 11487, 36564, 115327, 361194, 1124932, 3487857, 10774350, 33181365, 101924727, 312402600, 955728009, 2919095808, 8903220174, 27121002621, 82525328253, 250867833102, 761946207338, 2312406692839, 7012910929818, 21254741084817, 64381661704933

Offset

3,2

Links

Table of n, a(n) for n=3..30.

Jean-Luc Baril, Sergey Kirgizov, José L. Ramírez, and Diego Villamizar, The Combinatorics of Motzkin Polyominoes, arXiv:2401.06228 [math.CO], 2024. See Corollary 6.4 at pages 18-19.

Formula

a(n) = (3^n - 3*A002426(n))/2 - 2*A002426(n-1) + 2*A001006(n-1).

Mathematica

t[n_]:=SeriesCoefficient[1/(Sqrt[1-2x-3x^2]), {x, 0, n}]; (* A002426 *)
m[n_]:=SeriesCoefficient[(1 - x - (1 - 2x - 3x^2)^(1/2))/(2x^2), {x, 0, n}]; (* A001006 *)
a[n_]:=(3^n-3t[n])/2-2t[n-1]+2m[n-1]; Array[a, 28, 3]

Crossrefs

Cf. A001006, A002426, A369359.

Sequence in context: A277973 A143815 A209241 * A092491 A112308 A034336

Adjacent sequences: A369357 A369358 A369359 * A369361 A369362 A369363

Keyword

nonn

Author

Stefano Spezia, Jan 21 2024

Status

approved