OFFSET
1,2
COMMENTS
FORMULA
u(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2....3
4....9....8
7....24...33....21
12...54...109...111...55
First three polynomials u(n,x): 1, 2+ 3x, 4 + 9x + 8x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*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[%] (* A210747 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210748 *)
Table[u[n, x] /. x -> 1, {n, 1, z}] (* A002450 *)
Table[v[n, x] /. x -> 1, {n, 1, z}] (* A002450 *)
Table[u[n, x] /. x -> -1, {n, 1, z}] (* A077925 *)
Table[v[n, x] /. x -> -1, {n, 1, z}] (* A000012 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 25 2012
STATUS
approved