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

0,3

Links

Table of n, a(n) for n=0..27.

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

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

Prog

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

Crossrefs

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

Sequence in context: A149606 A363466 A019045 * A149607 A149608 A149609

Adjacent sequences: A191675 A191676 A191677 * A191679 A191680 A191681

Keyword

nonn

Author

Joerg Arndt, Jun 30 2011

Status

approved