A209153 Triangle of coefficients of polynomials u(n,x) jointly generated with A208340; see the Formula section.

1, 2, 1, 4, 5, 2, 7, 14, 11, 3, 11, 31, 38, 22, 5, 16, 60, 103, 93, 43, 8, 22, 106, 239, 298, 212, 81, 13, 29, 175, 497, 802, 782, 459, 150, 21, 37, 274, 952, 1909, 2393, 1917, 958, 273, 34, 46, 411, 1710, 4143, 6410, 6570, 4465, 1942, 491, 55, 56, 595

Offset

1,2

Comments

Every row ends with a Fibonacci number (A000045).

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

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)=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....1
4....5....2
7....14...11...3
11...31...38...22...5
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_] := 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[%]    (* A209153 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208340 *)

Crossrefs

Cf. A208340, A208510.

Sequence in context: A209146 A209154 A144332 * A209141 A038719 A376286

Adjacent sequences: A209150 A209151 A209152 * A209154 A209155 A209156

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 07 2012

Status

approved