OFFSET
1,2
COMMENTS
Row n begins with F(n+1) and ends with 2^(n-1), where F=A000045 (Fibonacci numbers).
Alternating row sums: 1,0,0,0,0,0,0,0,0,0,...
For a discussion and guide to related arrays, see A208510.
Riordan array ((1+x)/(1-x-x^2), (2x+x^2)/(1-x-x^2)). - Philippe Deléham, Mar 24 2012
Triangle given by (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 26 2012
FORMULA
u(n,x) = x*u(n-1,x) + (x+1)*v(n-1,x),
v(n,x) = (x+1)*u(n-1,x) + (x+1)*v(n-1,x),
where u(1,x)=1, v(1,x)=1.
T(n,k) = T(n-1,k) + 2*T(n-1,k-1) + T(n-2,k) + T(n-2,k-1), T(1,0) = 1, T(2,0) = T(2,1) = 2, T(n,k) = 0 if k < 0 or if k >= 0. - Philippe Deléham, Mar 24 2012
EXAMPLE
First five rows:
1;
2, 2;
3, 7, 4;
5, 17, 20, 8;
8, 37, 65, 52, 16;
First three polynomials v(n,x):
1
2 + 2x
3 + 7x + 4x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x];
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A209745 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209746 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 13 2012
STATUS
approved