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

1, 3, 1, 6, 6, 3, 11, 18, 18, 7, 19, 45, 63, 49, 17, 32, 100, 182, 200, 133, 41, 53, 208, 464, 658, 613, 356, 99, 87, 413, 1094, 1886, 2244, 1823, 944, 239, 142, 794, 2437, 4940, 7093, 7325, 5302, 2483, 577, 231, 1490, 5206, 12113, 20311, 25220

Offset

1,2

Comments

Row n starts with -2+F(n+3), where F=A000045 (Fibonacci numbers) and ends with A001333(n-1).

Alternating row sums: 1,2,3,4,5,6,7,8,...

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
3....1
6....6....3
11...18...18...7
19...45...63...49...17
First three polynomials v(n,x): 1, 3 + x, 6 + 6x +3x^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. A210743, A208510.

Sequence in context: A116412 A089511 A246257 * A242729 A112692 A291217

Adjacent sequences: A210741 A210742 A210743 * A210745 A210746 A210747

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 24 2012

Status

approved