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

1, 3, 2, 7, 8, 2, 15, 24, 12, 2, 31, 64, 48, 16, 2, 63, 160, 160, 80, 20, 2, 127, 384, 480, 320, 120, 24, 2, 255, 896, 1344, 1120, 560, 168, 28, 2, 511, 2048, 3584, 3584, 2240, 896, 224, 32, 2, 1023, 4608, 9216, 10752, 8064, 4032, 1344, 288, 36, 2, 2047

Offset

1,2

Comments

Column 1: -1+2^n.

Row sums: A048473.

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

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

Row sums without first column give A056182. - Alois P. Heinz, Jan 14 2022

Links

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

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....2
7....8....2
15...24...12...2
31...64...48...16...2
First three polynomials v(n,x): 1, 3 + 2x , 7 + 8x + 2x^2.

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. A210203, A208510.

Cf. A056182.

Sequence in context: A054183 A357939 A188656 * A208657 A329940 A074680

Adjacent sequences: A210201 A210202 A210203 * A210205 A210206 A210207

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 18 2012

Status

approved