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

1,2

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.

Links

Table of n, a(n) for n=1..53.

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.

Example

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

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 *)

Crossrefs

Cf. A210741, A208510.

Sequence in context: A173701 A116627 A254331 * A175056 A320274 A333398

Adjacent sequences: A210739 A210740 A210741 * A210743 A210744 A210745

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 24 2012

Status

approved