A127167 T(3n,2n), where T is the array in A047110.

1, 5, 73, 1348, 27811, 612728, 14103464, 334974405, 8146520511, 201822398131, 5074951075766, 129185072614240, 3322359273912432, 86191998671455630, 2252923797781463037, 59273686760263160137, 1568440076774389559527, 41713725234702452284249

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

G.f.: A(x) where (161051*x^2 +1088*x -64) * A(x)^10 + (4600*x -320) * A(x)^9 + (7276*x -624) * A(x)^8 + (7830*x -512) * A(x)^7 + (6189*x +68) * A(x)^6 + (2177*x + 540) * A(x)^5 + 535*A(x)^4 + 278*A(x)^3 + 84*A(x)^2 + 14*A(x) + 1 = 0. - Mark van Hoeij, May 01 2013

Example

T(h,k) counts lattice paths restricted as in A047110 by the line y=2x/3, so that the numbers T(3n,2n) are of interest.
T(3,2) counts these 5 paths: RRRUU, RRURU, URRRU, URURR, UURRR.

Maple

T:= proc(h, k) option remember;
      `if`([h, k]=[0, 0], 1, `if`(h<0 or k<0, 0, T(h-1, k)+
      `if`(3*k>2*h and 3*(k-1)<2*h, 0, T(h, k-1))))
    end:
a:= n-> T(3*n, 2*n):
seq (a(n), n=0..30); # Alois P. Heinz, Apr 04 2012
series(RootOf((161051*x^2+1088*x-64)*A^10 + (4600*x-320)*A^9 + (7276*x-624)*A^8 + (7830*x-512)*A^7 + (6189*x+68)*A^6 + (2177*x+540)*A^5 +535*A^4 +278*A^3 +84*A^2 +14*A +1, A), x=0, 30); # Mark van Hoeij, May 01 2013

Crossrefs

Cf. A047110.

Sequence in context: A182328 A222352 A159509 * A005259 A195636 A213111

Adjacent sequences: A127164 A127165 A127166 * A127168 A127169 A127170

Keyword

nonn

Author

Clark Kimberling, Jan 06 2007

Extensions

More terms from Alois P. Heinz, Apr 04 2012

Status

approved