A209146 Triangle of coefficients of polynomials u(n,x) jointly generated with A209147; see the Formula section.

1, 2, 1, 4, 5, 2, 7, 13, 11, 4, 12, 29, 34, 24, 8, 20, 60, 90, 85, 52, 16, 33, 118, 215, 255, 206, 112, 32, 54, 225, 481, 680, 683, 488, 240, 64, 88, 419, 1028, 1682, 1994, 1760, 1136, 512, 128, 143, 767, 2122, 3937, 5361, 5553, 4408, 2608, 1088, 256

Offset

1,2

Comments

Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,...

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

Links

Table of n, a(n) for n=1..55.

Formula

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

v(n,x)=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...1
4...5...2
7...13...11...4
12...29...34...24...8
First three polynomials v(n,x): 1, 2 + x, 4 + 5x + 2x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, 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[%]    (* A209146 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209147 *)

Crossrefs

Cf. A209146, A208510.

Sequence in context: A051176 A145064 A209166 * A209154 A144332 A209153

Adjacent sequences: A209143 A209144 A209145 * A209147 A209148 A209149

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 06 2012

Status

approved