A210041 Triangle of coefficients of polynomials u(n,x) jointly generated with A209758; see the Formula section.

1, 3, 5, 3, 7, 8, 6, 9, 15, 19, 12, 11, 24, 41, 44, 24, 13, 35, 74, 107, 100, 48, 15, 48, 120, 214, 270, 224, 96, 17, 63, 181, 380, 591, 664, 496, 192, 19, 80, 259, 622, 1137, 1576, 1600, 1088, 384, 21, 99, 356, 959, 2001, 3259, 4088, 3792, 2368, 768, 23

Offset

1,2

Comments

Row sums: even-indexed Fibonacci numbers: 1,3,8,21,55,...

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

Links

Table of n, a(n) for n=1..57.

Formula

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

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

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

Example

First five rows:
1
3
5...3
7...8....6
9...15...19...12
First three polynomials u(n,x): 1, 3, 5 + 3x.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 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[%]    (* A210041 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209758 *)

Crossrefs

Cf. A209758, A208510.

Sequence in context: A137768 A137769 A029602 * A345280 A240499 A248511

Adjacent sequences: A210038 A210039 A210040 * A210042 A210043 A210044

Keyword

nonn,tabf

Author

Clark Kimberling, Mar 17 2012

Status

approved