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

1, 3, 7, 1, 15, 5, 1, 31, 17, 6, 1, 63, 49, 24, 7, 1, 127, 129, 80, 32, 8, 1, 255, 321, 240, 120, 41, 9, 1, 511, 769, 672, 400, 170, 51, 10, 1, 1023, 1793, 1792, 1232, 620, 231, 62, 11, 1, 2047, 4097, 4608, 3584, 2072, 912, 304, 74, 12, 1, 4095, 9217

Offset: 1

Author

Clark Kimberling, Mar 17 2012

Keywords

• nonn
• tabf

Comments

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

Examples

			First five rows:
1
3
7....1
15...5....1
31...17...6...1
First three polynomials u(n,x): 1, 3, 7 + x.
		

Crossrefs

Cf. A210038, A208510.

Programs

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 *)

Formula

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,

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