A209165 Triangle of coefficients of polynomials v(n,x) jointly generated with A209164; see the Formula section.

1, 3, 1, 6, 4, 1, 12, 14, 7, 1, 24, 40, 28, 8, 1, 48, 104, 96, 44, 11, 1, 96, 256, 296, 184, 66, 12, 1, 192, 608, 848, 664, 316, 90, 15, 1, 384, 1408, 2304, 2176, 1296, 496, 120, 16, 1, 768, 3200, 6016, 6656, 4768, 2288, 736, 152, 19, 1, 1536, 7168, 15232

Offset

1,2

Comments

Alternating row sums: 1,2,3,4,5,6,7,8,9,10,11,...

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

Links

Table of n, a(n) for n=1..58.

Formula

u(n,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
6....4....1
12...14...7....1
24...40...28...8...1
First three polynomials v(n,x): 1, 3 + x, 6 + 4x + x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, 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[%]    (* A209164 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209165 *)

Crossrefs

Cf. A209164, A208510.

Sequence in context: A131415 A210230 A207615 * A121437 A078585 A116551

Adjacent sequences: A209162 A209163 A209164 * A209166 A209167 A209168

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 08 2012

Status

approved