A210214 Triangle of coefficients of polynomials v(n,x) jointly generated with A210213; see the Formula section.

1, 3, 1, 6, 5, 1, 11, 14, 7, 1, 19, 34, 25, 9, 1, 32, 74, 75, 39, 11, 1, 53, 152, 195, 139, 56, 13, 1, 87, 299, 468, 419, 231, 76, 15, 1, 142, 571, 1056, 1147, 791, 356, 99, 17, 1, 231, 1066, 2280, 2911, 2429, 1364, 519, 125, 19, 1, 375, 1956, 4755, 6991

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..59.

Formula

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

v(n,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
3....1
6....5....1
11...14...7....1
19...34...25...9...1
First three polynomials v(n,x): 1, 3 + x , 6 + 5x + 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_] := 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[%]    (* A210213 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210214 *)

Crossrefs

Cf. A210213, A208510.

Sequence in context: A355010 A153641 A133545 * A322427 A209149 A343062

Adjacent sequences: A210211 A210212 A210213 * A210215 A210216 A210217

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 19 2012

Status

approved