A210743 Triangle of coefficients of polynomials u(n,x) jointly generated with A210744; see the Formula section.

1, 2, 3, 4, 8, 7, 7, 20, 25, 17, 12, 43, 76, 75, 41, 20, 88, 194, 264, 216, 99, 33, 172, 458, 770, 861, 606, 239, 54, 327, 1016, 2038, 2811, 2691, 1667, 577, 88, 608, 2161, 5012, 8206, 9689, 8149, 4517, 1393, 143, 1112, 4447, 11699, 22057, 30830

Offset

1,2

Comments

Row n starts with -1+F(n), where F=A000045 (Fibonacci numbers), and ends with A001333(n). For a discussion and guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..51.

Formula

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

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

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

Example

First five rows:
1
2....3
4....8....7
7....20...25...17
12...43...76...75...41
First three polynomials u(n,x): 1, 2+ 3x, 4 + 8x + 7x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*u[n - 1, 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[%]      (* A210743 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]      (* A210744 *)

Crossrefs

Cf. A210744, A208510.

Sequence in context: A176077 A332778 A263694 * A210750 A036712 A036706

Adjacent sequences: A210740 A210741 A210742 * A210744 A210745 A210746

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 24 2012

Status

approved