A210229 Triangle of coefficients of polynomials u(n,x) jointly generated with A210230; see the Formula section.

1, 2, 1, 4, 3, 1, 7, 8, 4, 1, 12, 18, 13, 5, 1, 20, 38, 35, 19, 6, 1, 33, 76, 86, 59, 26, 7, 1, 54, 147, 197, 164, 91, 34, 8, 1, 88, 277, 430, 420, 281, 132, 43, 9, 1, 143, 512, 904, 1014, 792, 447, 183, 53, 10, 1, 232, 932, 1846, 2338, 2087, 1371, 673, 245, 64

Offset

1,2

Comments

Column 1: -1+F(n+1), where F=A000045 (Fibonacci numbers)

Alternating row sums: 1,1,2,2,3,3,4,4,5,5,...

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

Links

Table of n, a(n) for n=1..64.

Formula

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

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

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

Example

First five rows:
1
2....1
4....3....1
7....8....4....1
12...18...13...5...1
First three polynomials u(n,x): 1, 2 + x, 4 + 3x + x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*u[n - 1, 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[%]     (* A210229 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210230 *)

Crossrefs

Cf. A210230, A208510.

Sequence in context: A345123 A133805 A131254 * A210213 A305695 A211235

Adjacent sequences: A210226 A210227 A210228 * A210230 A210231 A210232

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved