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A108075
Triangle in A071945 with rows reversed.
0
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
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
KEYWORD
nonn,tabl,easy
AUTHOR
N. J. A. Sloane, Jun 05 2005
EXTENSIONS
More terms from Emeric Deutsch, Jun 06 2005
STATUS
approved