OFFSET
1,2
COMMENTS
Alternating row sums are signed Fibonacci numbers (A000045).
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
2...5...4
2...7...12...8
2...9...21...28...16
First five polynomials v(n,x):
1
2 + 2x
2 + 5x + 4x^2
2 + 7x + 12x^2 + 8x^3
2 + 9x + 21x^2 + 28x^3 + 16x^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_] := u[n - 1, x] + 2 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[%] (* A208511 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208512 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 28 2012
STATUS
approved