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A210751
Triangle of coefficients of polynomials u(n,x) jointly generated with A210752; see the Formula section.
3
1, 2, 2, 3, 6, 5, 4, 12, 19, 13, 5, 20, 46, 59, 34, 6, 30, 90, 166, 179, 89, 7, 42, 155, 370, 572, 533, 233, 8, 56, 245, 715, 1426, 1904, 1564, 610, 9, 72, 364, 1253, 3046, 5240, 6171, 4536, 1597, 10, 90, 516, 2044, 5845, 12237, 18561, 19581, 13031
OFFSET
1,2
COMMENTS
Row n starts with n and ends with F(2n-1), where F=A000045 (Fibonacci numbers).
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
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...2
3...6....5
4...12...19...13
5...20...46...59...34
First three polynomials u(n,x): 1, 2 + 2x, 3 + 6x + 5x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := (x + 1)*u[n - 1, x] + x*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[%] (* A210751 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210752 *)
CROSSREFS
Sequence in context: A207623 A116447 A137757 * A279791 A328744 A345706
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 25 2012
STATUS
approved