A210203 Triangle of coefficients of polynomials u(n,x) jointly generated with A210204; see the Formula section.

1, 3, 7, 2, 15, 10, 2, 31, 34, 14, 2, 63, 98, 62, 18, 2, 127, 258, 222, 98, 22, 2, 255, 642, 702, 418, 142, 26, 2, 511, 1538, 2046, 1538, 702, 194, 30, 2, 1023, 3586, 5630, 5122, 2942, 1090, 254, 34, 2, 2047, 8194, 14846, 15874, 11006, 5122, 1598, 322

Offset

1,2

Comments

Column 1: -1+2^n

Row sums: 3^(n-1)

Alternating row sums: 1,1,1,1,1,1,1,1,1,...

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

Links

Table of n, a(n) for n=1..54.

Formula

u(n,x)=u(n-1,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
3
7....2
15...10...2
31...34...14...2
First three polynomials u(n,x): 1, 3, 7 + 2x.

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+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[%]   (* A210203 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210204 *)

Crossrefs

Cf. A210204, A208510.

Sequence in context: A246377 A260421 A237427 * A318467 A324713 A245611

Adjacent sequences: A210200 A210201 A210202 * A210204 A210205 A210206

Keyword

nonn,tabf

Author

Clark Kimberling, Mar 18 2012

Status

approved