A210742 Triangle of coefficients of polynomials v(n,x) jointly generated with A210741; see the Formula section.

1, 3, 2, 5, 9, 5, 7, 20, 27, 13, 9, 35, 73, 80, 34, 11, 54, 151, 252, 234, 89, 13, 77, 269, 597, 837, 677, 233, 15, 104, 435, 1199, 2225, 2702, 1941, 610, 17, 135, 657, 2158, 4956, 7943, 8533, 5523, 1597, 19, 170, 943, 3590, 9796, 19387, 27435, 26479

Offset: 1

Author

Clark Kimberling, Mar 24 2012

Keywords

• nonn
• tabl

Comments

Row n starts with 2n-1 and ends with an odd-indexed

Fibonacci number.

Row sums: A035344

Alternate row sums: 1,1,1,1,1,1,1,1,...

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

Examples

			First five rows:
1
3...2
5...9....5
7...20...27...13
9...35...73...80...34
First three polynomials v(n,x): 1, 3 + 2x, 5 + 9x + 5x^2
		

Crossrefs

Cf. A210741, A208510.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%]     (* A210741 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210742 *)

Formula

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

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

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