A158524 Choulet-Curtz triangle with T(0,0)=1, T(n,n)=T(n,0).

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, 420, 7, 7, 14, 36, 88, 200, 420, 1192, 8, 8, 16, 42, 106, 252, 568, 1192, 3384, 9, 9, 18, 48, 124, 304, 716, 1612, 3384, 9608, 10, 10, 20, 54, 142, 356, 864, 2032, 4576, 9608

Offset

0,4

Comments

Row sums are in A078484.

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

Links

Table of n, a(n) for n=0..65.

Richard Choulet, Curtz-like transformation.

Formula

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

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

Example

Triangle begins
    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;

Crossrefs

Cf. A078484.

Cf. A159035, A159036. - Richard Choulet, Apr 03 2009

Sequence in context: A097521 A081668 A126615 * A054274 A053695 A210550

Adjacent sequences: A158521 A158522 A158523 * A158525 A158526 A158527

Keyword

nonn,tabl

Author

Philippe Deléham, Mar 20 2009

Status

approved