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

1, 3, 5, 3, 7, 8, 6, 9, 15, 19, 12, 11, 24, 41, 44, 24, 13, 35, 74, 107, 100, 48, 15, 48, 120, 214, 270, 224, 96, 17, 63, 181, 380, 591, 664, 496, 192, 19, 80, 259, 622, 1137, 1576, 1600, 1088, 384, 21, 99, 356, 959, 2001, 3259, 4088, 3792, 2368, 768, 23

Offset: 1

Author

Clark Kimberling, Mar 17 2012

Keywords

• nonn
• tabf

Comments

Row sums: even-indexed Fibonacci numbers: 1,3,8,21,55,...

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

Examples

			First five rows:
1
3
5...3
7...8....6
9...15...19...12
First three polynomials u(n,x): 1, 3, 5 + 3x.
		

Crossrefs

Cf. A209758, 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.