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
Keywords
Examples
For n=6 we have 5 paths: UDUDUD, UUDDUD, UDUUDD, UUUDDD and UUDUDD
Programs
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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 *)
Formula
G.f.: (1-x^3-sqrt((1-x^3)*(1-4*x^2-x^3)))/(2*x^2).