A209758 Triangle of coefficients of polynomials v(n,x) jointly generated with A210041; see the Formula section.

1, 1, 3, 1, 5, 6, 1, 7, 13, 12, 1, 9, 22, 32, 24, 1, 11, 33, 63, 76, 48, 1, 13, 46, 107, 170, 176, 96, 1, 15, 61, 166, 321, 440, 400, 192, 1, 17, 78, 242, 546, 912, 1104, 896, 384, 1, 19, 97, 337, 864, 1683, 2488, 2704, 1984, 768, 1, 21, 118, 453, 1296, 2865

Offset

1,3

Comments

Row sums: -1+(odd-indexed Fibonacci numbers)

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

Links

Table of n, a(n) for n=1..61.

Formula

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

v(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,

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

Example

First five rows:
1
1...3
1...5...6
1...7...13...12
1...9...22...32...24
First three polynomials v(n,x): 1, 1 + 3x , 1 + 5x + 6x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := x*u[n - 1, x] + 2 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[%]    (* A210041 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209758 *)

Crossrefs

Cf. A210041, A208510.

Sequence in context: A181641 A049266 A089028 * A134083 A210551 A113445

Adjacent sequences: A209755 A209756 A209757 * A209759 A209760 A209761

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 17 2012

Status

approved