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A210602
Triangle of coefficients of polynomials v(n,x) jointly generated with A210597; see the Formula section.
2
1, 3, 1, 6, 5, 2, 11, 14, 11, 4, 19, 34, 36, 24, 8, 32, 74, 101, 89, 52, 16, 53, 152, 251, 279, 214, 112, 32, 87, 299, 582, 769, 735, 504, 240, 64, 142, 571, 1279, 1961, 2208, 1872, 1168, 512, 128, 231, 1066, 2704, 4706, 6096, 6057, 4648, 2672, 1088
OFFSET
1,2
COMMENTS
For n>1, row n starts with F(n+3)-2, where F=A000045
(Fibonacci numbers), and ends with 2^(n-2).
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)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3....1
6....5....2
11...14...11...4
19...34...36...24...8
First three polynomials v(n,x): 1, 3 + x, 6 + 5x + 2x^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] + 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[%] (* A210597 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210602 *)
CROSSREFS
Sequence in context: A322427 A209149 A343062 * A210801 A153091 A210593
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 24 2012
STATUS
approved