OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
LINKS
G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened
FORMULA
u(n,x) = x*u(n-1,x) + v(n-1,x),
v(n,x) = u(n-1,x) + v(n-1,x) + 1,
where u(1,x)=1, v(1,x)=1.
G.f.: (1 + (1 - x)*t - t^2)/((1 - t)*(1 - (x + 1)*t + (x - 1)*t^2)) = 1 + 3*t + (5 + x)*t^2 + ... . - G. C. Greubel, Jan 03 2018
EXAMPLE
First five rows:
1;
3;
5, 1;
9, 2, 1;
15, 6, 2, 1;
First three polynomials v(n,x): 1, 3, 5 + x.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
v[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
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[%] (* A209421 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209422 *)
CoefficientList[CoefficientList[Series[(1 + (1 - x)*t - t^2)/((1 - t)*(1 - (x + 1)*t + (x - 1)*t^2)), {t, 0, 10}], t], x]// Flatten (* G. C. Greubel, Jan 03 2018 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 09 2012
STATUS
approved