A210038 Triangle of coefficients of polynomials v(n,x) jointly generated with A210037; see the Formula section.

1, 3, 1, 7, 4, 1, 15, 12, 5, 1, 31, 32, 18, 6, 1, 63, 80, 56, 25, 7, 1, 127, 192, 160, 88, 33, 8, 1, 255, 448, 432, 280, 129, 42, 9, 1, 511, 1024, 1120, 832, 450, 180, 52, 10, 1, 1023, 2304, 2816, 2352, 1452, 681, 242, 63, 11, 1, 2047, 5120, 6912, 6400

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

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

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

Example

First five rows:
1
3....1
7....4....1
15...12...5....1
31...32...18...6...1
First three polynomials v(n,x): 1, 3 + x , 7 + 4x + x^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_] := 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[%]    (* A210037 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210038 *)

Crossrefs

Cf. A210037, A208510.

Sequence in context: A104709 A110814 A275599 * A319076 A286513 A193970

Adjacent sequences: A210035 A210036 A210037 * A210039 A210040 A210041

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 17 2012

Status

approved