A210563 Triangle of coefficients of polynomials u(n,x) jointly generated with A210564; see the Formula section.

1, 1, 2, 1, 3, 5, 1, 3, 10, 13, 1, 3, 11, 32, 34, 1, 3, 11, 40, 99, 89, 1, 3, 11, 41, 141, 299, 233, 1, 3, 11, 41, 152, 482, 887, 610, 1, 3, 11, 41, 153, 556, 1604, 2595, 1597, 1, 3, 11, 41, 153, 570, 1998, 5217, 7508, 4181, 1, 3, 11, 41, 153, 571, 2113, 7042

Offset

1,3

Comments

Last terms in rows: odd-indexed Fibonacci numbers

Limiting row: A001835

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

Links

Table of n, a(n) for n=1..63.

Formula

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

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

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

Example

First five rows:
1
1...2
1...3...5
1...3...10...13
1...3...11...32...34
First three polynomials u(n,x): 1, 1 + 2x, 1 + 3x + 5x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%]  (* A210563 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A210564 *)

Crossrefs

Cf. A210564, A208510.

Sequence in context: A089984 A284429 A062105 * A236311 A347773 A368563

Adjacent sequences: A210560 A210561 A210562 * A210564 A210565 A210566

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 23 2012

Status

approved