A210802 Triangle of coefficients of polynomials v(n,x) jointly generated with A210801; see the Formula section.

1, 2, 2, 5, 5, 3, 8, 16, 11, 5, 17, 34, 40, 22, 8, 26, 82, 107, 93, 43, 13, 53, 163, 287, 287, 201, 81, 21, 80, 352, 674, 862, 709, 419, 150, 34, 161, 676, 1592, 2272, 2326, 1641, 845, 273, 55, 242, 1378, 3482, 5878, 6797, 5863, 3638, 1666, 491, 89, 485

Offset

1,2

Comments

Row n ends with F(n+1), where F=A000045 (Fibonacci numbers).

Row sums: A003462

Alternating row sums: A077898

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

Links

Table of n, a(n) for n=1..56.

Formula

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

v(n,x)=(x+2)*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....2
5....5....3
8....16...11...5
17...34...40...22...8
First three polynomials v(n,x): 1, 2 + 2x, 5 + 5x + 3x^2

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
d[x_] := h + x; e[x_] := p + x;
v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
j = 1; c = 1; h = 2; p = -1; f = 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[%]   (* A210801 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210802 *)
Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A003462 *)
Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A003462 *)
Table[u[n, x] /. x -> -1, {n, 1, z}] (* A000027 *)
Table[v[n, x] /. x -> -1, {n, 1, z}] (* A077898 *)

Crossrefs

Cf. A210801, A208510.

Sequence in context: A243941 A161622 A116559 * A257943 A008280 A239005

Adjacent sequences: A210799 A210800 A210801 * A210803 A210804 A210805

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 27 2012

Status

approved