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A210599
Triangle of coefficients of polynomials v(n,x) jointly generated with A210221; see the Formula section.
3
1, 2, 3, 3, 8, 8, 4, 16, 28, 21, 5, 26, 69, 92, 55, 6, 39, 134, 268, 290, 144, 7, 54, 233, 606, 974, 888, 377, 8, 72, 368, 1196, 2510, 3378, 2662, 987, 9, 92, 550, 2122, 5541, 9760, 11313, 7852, 2584, 10, 115, 780, 3510, 10900, 23825, 36188, 36872
OFFSET
1,2
COMMENTS
Row n starts with n and ends with an even-indexed Fibonacci number. For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=(x+1)*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...3
3...8....8
4...16...28...21
5...26...69...92...55
First three polynomials v(n,x): 1, 2 + 3x, 3 + 8x + 8x^2
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%] (* A210598 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210599 *)
CROSSREFS
Sequence in context: A193997 A330048 A210752 * A211879 A308774 A308859
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 24 2012
STATUS
approved