A210598 Triangle of coefficients of polynomials u(n,x) jointly generated with A210599; see the Formula section.

1, 2, 2, 3, 7, 5, 4, 14, 23, 13, 5, 24, 58, 72, 34, 6, 36, 119, 219, 219, 89, 7, 51, 209, 521, 777, 653, 233, 8, 68, 338, 1048, 2101, 2639, 1918, 610, 9, 88, 508, 1902, 4754, 7989, 8679, 5567, 1597, 10, 110, 730, 3180, 9565, 20055, 29062, 27844, 16003

Offset: 1

Author

Clark Kimberling, Mar 24 2012

Keywords

• nonn
• tabl

Comments

Row n starts with n and ends with an odd-indexed

Fibonacci number. For a discussion and guide to related

arrays, see A208510.

Examples

			First five rows:
1
2...2
3...7....5
4...14...23...13
5...24...58...72...34
First three polynomials u(n,x): 1, 2+ 2x, 3 + 7x + 5x^2.
		

Crossrefs

Cf. A210599, A208510.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%]    (* A210598 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210599 *)

Formula

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

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

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