A210741 Triangle of coefficients of polynomials u(n,x) jointly generated with A210742; see the Formula section.

1, 1, 3, 1, 5, 8, 1, 7, 19, 21, 1, 9, 34, 65, 55, 1, 11, 53, 141, 210, 144, 1, 13, 76, 257, 534, 654, 377, 1, 15, 103, 421, 1111, 1905, 1985, 987, 1, 17, 134, 641, 2041, 4447, 6512, 5911, 2584, 1, 19, 169, 925, 3440, 9038, 16837, 21557, 17345, 6765, 1

Offset

1,3

Comments

Rows end with even-indexed Fibonacci numbers

Row sums: A007070

Alternating row sums: signed powers of 2

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

Links

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

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
1...3
1...5...8
1...7...19...21
1...9...34...65...55
First three polynomials u(n,x): 1, 1+ 3x, 1 + 5x + 8x^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. A210742, A208510.

Sequence in context: A302191 A261712 A038738 * A208760 A340156 A340242

Adjacent sequences: A210738 A210739 A210740 * A210742 A210743 A210744

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 24 2012

Status

approved