A210798 Triangle of coefficients of polynomials v(n,x) jointly generated with A210797; see the Formula section.

1, 2, 2, 1, 3, 3, 2, 5, 7, 5, 1, 6, 12, 13, 8, 2, 8, 20, 29, 25, 13, 1, 9, 27, 51, 62, 46, 21, 2, 11, 39, 84, 125, 129, 84, 34, 1, 12, 48, 126, 224, 284, 258, 151, 55, 2, 14, 64, 182, 374, 562, 622, 505, 269, 89, 1, 15, 75, 250, 580, 1008, 1328, 1315, 969, 475

Offset

1,2

Comments

Row n starts with A109613(n) and ends with F(n+1), where F=A000045 (Fibonacci numbers).

Column 2: A114113

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

Links

Table of n, a(n) for n=1..65.

Formula

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

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

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

Example

First five rows:
1
2...2
1...3...3
2...5...7....5
1...6...12...13...8
First three polynomials v(n,x): 1, 2 + 2x, 1 + 3x + 3x^2

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
d[x_] := h + x; e[x_] := p + x;
v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
j = 0; c = 0; h = 2; p = -1; f = 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[%]    (* A210797 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210798 *)
Table[u[n, x] /. x -> 1, {n, 1, z}]   (* A099232 *)
Table[v[n, x] /. x -> 1, {n, 1, z}]   (* A006130 *)
Table[u[n, x] /. x -> -1, {n, 1, z}]  (* A008346 *)
Table[v[n, x] /. x -> -1, {n, 1, z}]  (* A039834 *)

Crossrefs

Cf. A210797, A208510.

Sequence in context: A321783 A327035 A177352 * A117501 A117915 A294453

Adjacent sequences: A210795 A210796 A210797 * A210799 A210800 A210801

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 26 2012

Status

approved