A209770 Triangle of coefficients of polynomials v(n,x) jointly generated with A209769; see the Formula section.

1, 3, 1, 5, 4, 2, 9, 12, 10, 3, 15, 29, 33, 19, 5, 25, 64, 93, 77, 37, 8, 41, 132, 234, 251, 171, 69, 13, 67, 261, 548, 719, 629, 362, 127, 21, 109, 500, 1216, 1884, 2004, 1482, 742, 230, 34, 177, 936, 2592, 4628, 5784, 5196, 3342, 1482, 412, 55, 287

Offset

1,2

Comments

Column 1: A001595

Row n ends with F(n), where F=A000045, the Fibonacci numbers.

Row sums: 1,4,11,34,101,304,911,2734,... A060925

Alternating row sums: 1,2,3,4,5,6,7,.... A000027

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

Links

Table of n, a(n) for n=1..56.

Formula

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

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
5....4....2
9....12...10...3
15...29...33...19...5
First three polynomials v(n,x): 1, 3 + x , 5 + 4x + 2x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
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[%]    (* A209769 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209770 *)

Crossrefs

Cf. A209669, A208510.

Sequence in context: A016574 A210560 A208922 * A210799 A068512 A011090

Adjacent sequences: A209767 A209768 A209769 * A209771 A209772 A209773

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 15 2012

Status

approved