A208512 Triangle of coefficients of polynomials v(n,x) jointly generated with A208511; see the Formula section.

1, 2, 2, 2, 5, 4, 2, 7, 12, 8, 2, 9, 21, 28, 16, 2, 11, 32, 58, 64, 32, 2, 13, 45, 101, 152, 144, 64, 2, 15, 60, 159, 296, 384, 320, 128, 2, 17, 77, 234, 513, 824, 944, 704, 256, 2, 19, 96, 328, 822, 1554, 2208, 2272, 1536, 512, 2, 21, 117, 443, 1244, 2685

Offset: 1

Author

Clark Kimberling, Feb 28 2012

Keywords

• nonn
• tabl

Comments

Alternating row sums are signed Fibonacci numbers (A000045).

Examples

			First five rows:
1
2...2
2...5...4
2...7...12...8
2...9...21...28...16
First five polynomials v(n,x):
1
2 + 2x
2 + 5x + 4x^2
2 + 7x + 12x^2 + 8x^3
2 + 9x + 21x^2 + 28x^3 + 16x^4
		

Crossrefs

Cf. A208511.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 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[%]  (* A208511 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208512 *)

Formula

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

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

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