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Triangle in A071945 with rows reversed.
0

%I #16 Jan 25 2020 02:34:00

%S 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,

%T 51,11,1,1697,1697,1153,609,249,73,13,1,6847,6847,4719,2591,1151,399,

%U 99,15,1,28161,28161,19617,11073,5201,2001,601,129,17,1,117631,117631,82623

%N Triangle in A071945 with rows reversed.

%H D. Baccherini, D. Merlini and R. Sprugnoli, <a href="http://pefmath.etf.rs/vol2num1/AADM-Vol2-No1-69-91.pdf">Level generating trees and proper Riordan arrays</a>, Applicable Analysis and Discrete Mathematics, 2, 2008, 69-91 (see p. 88). [From _Emeric Deutsch_, Sep 21 2008]

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

%F 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

%e Triangle begins:

%e 1;

%e 1, 1;

%e 3, 3, 1;

%e 9, 9, 5, 1;

%e 31, 31, 19, 7, 1;

%e ...

%p 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

%Y Row sums yield A052705. Column 0 yields A052709.

%K nonn,tabl,easy

%O 0,4

%A _N. J. A. Sloane_, Jun 05 2005

%E More terms from _Emeric Deutsch_, Jun 06 2005