A191678 Number of lattice paths from (0,0) to (n,n) using steps (1,0), (1,1), (0,2), (2,2).

1, 1, 5, 15, 62, 233, 937, 3729, 15121, 61492, 251942, 1036215, 4279754, 17731181, 73670725, 306823695, 1280574706, 5354602495, 22426876445, 94070238840, 395106054632, 1661489413472, 6994494531010, 29474635716345, 124319047552309, 524797934104312, 2217091297558466, 9373180869094923

Offset: 0

Author

Joerg Arndt, Jun 30 2011

Keywords

• nonn

Crossrefs

Cf. A001850, A026641, A036355, A137644, A192364, A192365, A192369, A191354.

Programs

Maple

P := (4*x^6+12*x^5-20*x^3+27*x^2+12*x-4)*A^3-(3*x^2+3*x-3)*A+1;
Q := eval(P, A=A+1):
series(RootOf(Q,A)+1, x=0, 30);  # Mark van Hoeij, Apr 17 2013

PARI

/* same as in A092566 but use */
steps=[[1,0], [1,1], [0,2], [2,2]];
/* Joerg Arndt, Jun 30 2011 */

Formula

G.f.: A(x) where (4*x^6+12*x^5-20*x^3+27*x^2+12*x-4)*A(x)^3-(3*x^2+3*x-3)*A(x)+1 = 0. - Mark van Hoeij, Apr 17 2013