A108075 Triangle in A071945 with rows reversed.

1, 1, 1, 3, 3, 1, 9, 9, 5, 1, 31, 31, 19, 7, 1, 113, 113, 73, 33, 9, 1, 431, 431, 287, 143, 51, 11, 1, 1697, 1697, 1153, 609, 249, 73, 13, 1, 6847, 6847, 4719, 2591, 1151, 399, 99, 15, 1, 28161, 28161, 19617, 11073, 5201, 2001, 601, 129, 17, 1, 117631, 117631, 82623

Offset

0,4

Links

Table of n, a(n) for n=0..57.

D. Baccherini, D. Merlini and R. Sprugnoli, Level generating trees and proper Riordan arrays, Applicable Analysis and Discrete Mathematics, 2, 2008, 69-91 (see p. 88). [From Emeric Deutsch, Sep 21 2008]

Formula

G.f.: (1-q)/(z(1+z)(2-t+tq)), where q = sqrt(1 - 4z - 4z^2). - Emeric Deutsch, Jun 06 2005

T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n,k+1), T(0,0)=1. - Philippe Deléham, Nov 18 2009

Example

Triangle begins:
   1;
   1,  1;
   3,  3,  1;
   9,  9,  5, 1;
  31, 31, 19, 7, 1;
  ...

Maple

q:=sqrt(1-4*z-4*z^2): G:=(1-q)/z/(1+z)/(2-t+t*q): Gser:=simplify(series(G, z=0, 13)): P[0]:=1: for n from 1 to 10 do P[n]:=coeff(Gser, z^n) od: for n from 0 to 10 do seq(coeff(t*P[n], t^k), k=1..n+1) od; # yields sequence in triangular form - Emeric Deutsch, Jun 06 2005

Crossrefs

Row sums yield A052705. Column 0 yields A052709.

Sequence in context: A221712 A193741 A193824 * A215120 A084145 A122919

Adjacent sequences: A108072 A108073 A108074 * A108076 A108077 A108078

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane, Jun 05 2005

Extensions

More terms from Emeric Deutsch, Jun 06 2005

Status

approved