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

1,2

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.

Links

Table of n, a(n) for n=1..60.

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.

Example

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.

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 *)

Crossrefs

Cf. A210187, A208510.

Sequence in context: A260161 A195694 A021451 * A183442 A296019 A134232

Adjacent sequences: A210185 A210186 A210187 * A210189 A210190 A210191

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 18 2012

Status

approved