OFFSET
1,5
COMMENTS
Alternating row sums: 1,0,1,0,1,0,1,0,...
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=2x*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
1...1
1...3....3
1...6....10...5
1...10...22...23...11
First five polynomials u(n,x):
1
1 + x
1 + 3x + 3x^2
1 + 6x + 10x^2 + 5x^3
1 + 10x + 22x^2 + 23x^3 + 11x^4
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 2 x*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[%] (* A208524 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208525 *)
Table[u[n, x] /. x -> 1, {n, 1, z}] (*A060816*)
Table[v[n, x] /. x -> 1, {n, 1, z}] (*|A084244|*)
Table[u[n, x] /. x -> -1, {n, 1, z}](*alt. row sums*)
Table[v[n, x] /. x -> -1, {n, 1, z}](*alt. row sums*)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 29 2012
STATUS
approved