A158524 - OEIS

%I #10 Jan 28 2018 02:46:05

%S 1,1,1,2,2,2,6,3,3,6,18,4,4,8,18,52,5,5,10,24,52,148,6,6,12,30,70,148,

%T 420,7,7,14,36,88,200,420,1192,8,8,16,42,106,252,568,1192,3384,9,9,18,

%U 48,124,304,716,1612,3384,9608,10,10,20,54,142,356,864,2032,4576,9608

%N Choulet-Curtz triangle with T(0,0)=1, T(n,n)=T(n,0).

%C Row sums are in A078484.

%C This sequence is an example of a sequence u(n) which satisfies (using the notation from the link): T_{1,1}(u(0), u(1), u(2), u(3), ...) = (u(1), u(2), u(3), ...). The o.g.f of all such sequences is given by the formula Phi(z)=u(0)*((1-3*z+2*z^2-z^3)/(1-4*z+4*z^2-2*z^3))+((z+z^3)/(1-4*z+4*z^2-2*z^3)) with u(0) in N or Z; the sequences are given by u(n) = u(0)*(1, 1, 2, 5, 14, 40, 114, 324, 920, ...) + (0, 1, 4, 13, 38, 108, 868, 2464, 6996, ...), i.e., u(n) = u(0)*A159035(n) + A159036(n). - _Richard Choulet_, Apr 03 2009

%H Richard Choulet, <a href="http://www.apmep.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation</a>.

%F T(n,k) = T(n-1,k) + T(k-1,k-1), k >= 1, n > k;

%F T(n,n) = T(n,0) = Sum_{k=0..n} T(n-1,k); T(0,0)=1.

%e Triangle begins

%e     1;

%e     1,   1;

%e     2,   2,   2;

%e     6,   3,   3,   6;

%e    18,   4,   4,   8,  18;

%e    52,   5,   5,  10,  24,  52;

%e   148,   6,   6,  12,  30,  70, 148;

%Y Cf. A078484.

%Y Cf. A159035, A159036. - _Richard Choulet_, Apr 03 2009

%K nonn,tabl

%O 0,4

%A _Philippe Deléham_, Mar 20 2009