A209758 Triangle of coefficients of polynomials v(n,x) jointly generated with A210041; see the Formula section.

1, 1, 3, 1, 5, 6, 1, 7, 13, 12, 1, 9, 22, 32, 24, 1, 11, 33, 63, 76, 48, 1, 13, 46, 107, 170, 176, 96, 1, 15, 61, 166, 321, 440, 400, 192, 1, 17, 78, 242, 546, 912, 1104, 896, 384, 1, 19, 97, 337, 864, 1683, 2488, 2704, 1984, 768, 1, 21, 118, 453, 1296, 2865

Offset: 1

Author

Clark Kimberling, Mar 17 2012

Keywords

• nonn
• tabl

Comments

Row sums: -1+(odd-indexed Fibonacci numbers)

For a discussion and guide to related arrays, see A208510.

Examples

			First five rows:
1
1...3
1...5...6
1...7...13...12
1...9...22...32...24
First three polynomials v(n,x): 1, 1 + 3x , 1 + 5x + 6x^2.
		

Crossrefs

Cf. A210041, A208510.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := x*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[%]    (* A210041 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209758 *)

Formula

u(n,x)=u(n-1,x)+v(n-1,x)+1,

v(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.