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A210752
Triangle of coefficients of polynomials v(n,x) jointly generated with A210751; see the Formula section.
3
1, 2, 3, 3, 8, 8, 4, 15, 27, 21, 5, 24, 61, 86, 55, 6, 35, 114, 227, 265, 144, 7, 48, 190, 484, 799, 798, 377, 8, 63, 293, 905, 1910, 2703, 2362, 987, 9, 80, 427, 1546, 3951, 7150, 8874, 6898, 2584, 10, 99, 596, 2471, 7391, 16188, 25711, 28455, 19929
OFFSET
1,2
COMMENTS
Row n starts with n and ends with F(2n), 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...3
3...8....8
4...15...27...21
5...24...61...86...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 + 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: A256679 A193997 A330048 * A210599 A211879 A308774
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 25 2012
STATUS
approved