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A257517 Number of 3-generalized 2-Motzkin paths of length n with no level steps H=(3,0) at even level. 0
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 (list; graph; refs; listen; history; text; internal format)
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).

Conjecture: +(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: A077902 A005834 A052531 * A095005 A209066 A208938

Adjacent sequences:  A257514 A257515 A257516 * A257518 A257519 A257520

KEYWORD

nonn

AUTHOR

José Luis Ramírez Ramírez, Apr 27 2015

STATUS

approved

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Last modified May 30 18:38 EDT 2020. Contains 334728 sequences. (Running on oeis4.)