A210192 Triangle of coefficients of polynomials v(n,x) jointly generated with A210191; see the Formula section.

1, 1, 3, 1, 7, 3, 1, 11, 13, 3, 1, 15, 31, 19, 3, 1, 19, 57, 63, 25, 3, 1, 23, 91, 151, 107, 31, 3, 1, 27, 133, 299, 321, 163, 37, 3, 1, 31, 183, 523, 771, 591, 231, 43, 3, 1, 35, 241, 839, 1593, 1683, 985, 311, 49, 3, 1, 39, 307, 1263, 2955, 4047, 3259, 1527

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..63.

Formula

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

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

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

Example

First five rows:
1
1...3
1...7....3
1...11...13...3
1...15...31...19...3
First three polynomials v(n,x): 1, 1 + 3x , 1 + 7x + 3x^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_] := 2 x*u[n - 1, x] + 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[%]   (* A210191 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210192 *)

Crossrefs

Cf. A210191, A208510.

Sequence in context: A059090 A327990 A133115 * A249755 A249248 A104797

Adjacent sequences: A210189 A210190 A210191 * A210193 A210194 A210195

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 18 2012

Status

approved