A209148 Triangle of coefficients of polynomials u(n,x) jointly generated with A209149; see the Formula section.

1, 2, 1, 5, 5, 1, 11, 16, 7, 1, 23, 44, 30, 9, 1, 47, 112, 104, 48, 11, 1, 95, 272, 320, 200, 70, 13, 1, 191, 640, 912, 720, 340, 96, 15, 1, 383, 1472, 2464, 2352, 1400, 532, 126, 17, 1, 767, 3328, 6400, 7168, 5152, 2464, 784, 160, 19, 1, 1535, 7424

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

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

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

T(n,k) = 3*T(n-1,k)+T(n-1,k-1)-2*T(n-2,k)-T(n-2,k-1), T(1,0)=T(2,1)=T(3,2)=1, T(2,0)=2, T(3,0)=T(3,1)=5, T(n,k)=0 if k<0 or if k>=n. - Philippe Deléham, Jan 17 2014

Example

First five rows:
  1
  2....1
  5....5....1
  11...16...7....1
  23...44...30...9...1
First three polynomials v(n,x): 1, 2 + x, 5 + 5x + x^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] + (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[%]    (* A209148 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209149 *)

Crossrefs

Cf. A209149, A208510.

Sequence in context: A204111 A079502 A209164 * A126124 A123971 A060920

Adjacent sequences: A209145 A209146 A209147 * A209149 A209150 A209151

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 07 2012

Extensions

Example corrected by Philippe Deléham, Jan 17 2014

Status

approved