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A210738
Triangle of coefficients of polynomials v(n,x) jointly generated with A210603; see the Formula section.
3
1, 3, 2, 6, 9, 4, 11, 25, 23, 8, 19, 60, 81, 55, 16, 32, 130, 237, 233, 127, 32, 53, 266, 610, 798, 625, 287, 64, 87, 522, 1451, 2364, 2439, 1601, 639, 128, 142, 995, 3255, 6373, 8138, 6984, 3969, 1407, 256, 231, 1855, 6995, 16007, 24430, 25832
OFFSET
1,2
COMMENTS
Row n starts with F(n+3)-2, where F=A000045 (Fibonacci
numbers), and ends with 2^(n-1). For a discussion and
guide to related arrays, see A208510.
FORMULA
u(n,x)=2x*u(n-1,x)+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
3....2
6....9....4
11...25...23...8
19...60...81...55...16
First three polynomials v(n,x): 1, 3 + 2x, 6 + 9x + 4x^2
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := 2 x*u[n - 1, x] + 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[%] (* A210603 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210738 *)
CROSSREFS
Sequence in context: A318049 A352877 A210754 * A210601 A197493 A300070
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 24 2012
STATUS
approved