A209154 Triangle of coefficients of polynomials u(n,x) jointly generated with A209157; see the Formula section.

1, 2, 1, 4, 5, 2, 7, 14, 10, 2, 11, 32, 36, 18, 4, 16, 65, 104, 82, 32, 4, 22, 121, 258, 282, 168, 52, 8, 29, 210, 574, 820, 676, 328, 88, 8, 37, 344, 1176, 2116, 2264, 1504, 608, 136, 16, 46, 537, 2256, 4980, 6640, 5672, 3136, 1096, 224, 16, 56, 805

Offset

1,2

Comments

Last number in each row is a power of 2.

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

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

Links

Table of n, a(n) for n=1..57.

Formula

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

v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.

Example

First five rows:
1
2....1
4....5....2
7....14...10...2
11...32...36...18...4
First three polynomials v(n,x): 1, 2 + x, 4 + 5x + 2x^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_] := 2 x*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[%]    (* A209154 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209157 *)

Crossrefs

Cf. A209157, A208510.

Sequence in context: A145064 A209166 A209146 * A144332 A209153 A209141

Adjacent sequences: A209151 A209152 A209153 * A209155 A209156 A209157

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 07 2012

Status

approved