A210188 Triangle of coefficients of polynomials v(n,x) jointly generated with A210187; see the Formula section.

1, 2, 2, 3, 7, 2, 4, 16, 11, 2, 5, 30, 36, 15, 2, 6, 50, 91, 64, 19, 2, 7, 77, 196, 204, 100, 23, 2, 8, 112, 378, 540, 385, 144, 27, 2, 9, 156, 672, 1254, 1210, 650, 196, 31, 2, 10, 210, 1122, 2640, 3289, 2366, 1015, 256, 35, 2, 11, 275, 1782, 5148, 8008

Offset: 1

Author

Clark Kimberling, Mar 18 2012

Keywords

• nonn
• tabl

Comments

Row sums: -1+(odd-indexed Fibonacci numbers): 1,4,12,...

Period of alternating row sums: (1,-,-2,-3,-2,0)

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

Examples

			First five rows:
1
2...2
3...7....2
4...16...11...2
5...30...36...15...2
First three polynomials v(n,x): 1, 2 + 2x , 3 + 7x + 2x^2.
		

Crossrefs

Cf. A210187, 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] + (x + 1)*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[%]    (* A210187 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210188 *)

Formula

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

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

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