A257516 Number of 3-generalized Motzkin paths of length n with no level steps H=(3,0) at even level.

1, 0, 1, 0, 2, 1, 5, 4, 15, 15, 48, 57, 162, 218, 570, 842, 2070, 3284, 7709, 12922, 29299, 51255, 113220, 204781, 443574, 823554, 1757947, 3331818, 7035054, 13552699, 28387680, 55401396, 115369417, 227501256, 471780468, 938107057, 1939727280, 3883120002

Offset

0,5

Links

Table of n, a(n) for n=0..37.

Formula

G.f.: (1-x^3-sqrt((1-x^3)*(1-4*x^2-x^3)))/(2*x^2).

Example

For n=6 we have 5 paths: UDUDUD, UUDDUD, UDUUDD, UUUDDD and UUDUDD

Mathematica

CoefficientList[Series[(1-x^3-Sqrt[(1-x^3)*(1-4*x^2-x^3)])/(2*x^2), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 27 2015 *)

Crossrefs

Cf. A002212, A090345.

Sequence in context: A240607 A304298 A309976 * A346800 A124660 A217104

Adjacent sequences: A257513 A257514 A257515 * A257517 A257518 A257519

Keyword

nonn

Author

José Luis Ramírez Ramírez, Apr 27 2015

Status

approved