A209706 Triangle of coefficients of polynomials v(n,x) jointly generated with A209705; see the Formula section.

1, 3, 2, 4, 7, 4, 5, 14, 18, 8, 6, 23, 46, 44, 16, 7, 34, 92, 136, 104, 32, 8, 47, 160, 320, 376, 240, 64, 9, 62, 254, 640, 1016, 992, 544, 128, 10, 79, 378, 1148, 2296, 3024, 2528, 1216, 256, 11, 98, 536, 1904, 4592, 7616, 8576, 6272, 2688, 512, 12, 119

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..57.

Formula

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

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

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

T(n,k) = 2*T(n-1,k)+2*T(n-1,k-1)-T(n-2,k)-2*T(n-2,k-1), T(1,0)=1, T(2,0)=3, T(2,1)=2, T(3,0)=4, T(3,1)=7, T(3,2)=4, T(n,k)=0 if k<0 or if k>=n. - Philippe Deléham, Dec 27 2013

Example

First five rows:
1
3...2
4...7....4
5...14...18...8
6...23...46...44...16
First three polynomials v(n,x): 1, 3 + 2x , 4 + 7x + 4x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := (x + 1)*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[%]  (* A209705 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A209706 *)

Crossrefs

Cf. A209705, A208510.

Sequence in context: A123097 A368218 A352419 * A350077 A134571 A054086

Adjacent sequences: A209703 A209704 A209705 * A209707 A209708 A209709

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 12 2012

Status

approved