OFFSET
1,2
COMMENTS
Alternating row sums: 1,3,2,2,2,2,2,2,2,2,2,2,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+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.
EXAMPLE
First five rows:
1
3...1
4...2...3
5...5...2
6...9...7...2
First three polynomials v(n,x): 1, 3 + x , 4 + 2x + 3x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + 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[%] (* A115241 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209688 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 12 2012
STATUS
approved