A257517 Number of 3-generalized 2-Motzkin paths of length n with no level steps H=(3,0) at even level.

1, 0, 1, 0, 2, 2, 5, 8, 18, 30, 66, 120, 252, 484, 1005, 1984, 4110, 8278, 17150, 35024, 72748, 150012, 312642, 649424, 1358244, 2837484, 5954980, 12497616, 26313432, 55434248, 117062205, 247412928, 523881238, 1110335334, 2356819254, 5007428384, 10652412108, 22682131308, 48349084054, 103150869360, 220276819836

Offset

0,5

Links

Table of n, a(n) for n=0..40.

Formula

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

D-finite with recurrence +(n+2)*(n^2-n+3)*a(n) +(n+1)*(n^2+1)*a(n-1) -4*(n-1)*(n^2-n+3)*a(n-2) +2*(-4*n^3+11*n^2-13*n+19)*a(n-3) -2*(2*n-7)*(n^2+1)*a(n-4) +4*(2*n-11)*(n^2-n+3)*a(n-5) +4*(3*n^3-21*n^2+12*n-34)*a(n-6) +4*(n-8)*(n^2+1)*a(n-7)=0. - R. J. Mathar, Jun 07 2016

Mathematica

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

Crossrefs

Cf. A257516, A005572, A025266.

Sequence in context: A005834 A367717 A052531 * A337079 A095005 A209066

Adjacent sequences: A257514 A257515 A257516 * A257518 A257519 A257520

Keyword

nonn,easy

Author

José Luis Ramírez Ramírez, Apr 27 2015

Status

approved