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A210231 Triangle of coefficients of polynomials u(n,x) jointly generated with A210232; see the Formula section. 3
1, 2, 1, 3, 4, 1, 4, 8, 7, 1, 5, 14, 18, 11, 1, 6, 21, 39, 36, 16, 1, 7, 30, 69, 93, 66, 22, 1, 8, 40, 114, 192, 199, 113, 29, 1, 9, 52, 172, 360, 474, 393, 183, 37, 1, 10, 65, 250, 610, 997, 1068, 729, 283, 46, 1, 11, 80, 345, 980, 1882, 2501, 2238, 1285, 421 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..64.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...1

3...4....1

4...8....7....1

5...14...18...11...1

First three polynomials u(n,x): 1, 2 + x, 3 + 4x + x^2.

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;

v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%]     (* A210231 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]     (* A210232 *)

CROSSREFS

Cf. A210232, A208510.

Sequence in context: A072506 A188236 A181851 * A180378 A208341 A201634

Adjacent sequences:  A210228 A210229 A210230 * A210232 A210233 A210234

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 20 2012

STATUS

approved

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Last modified October 22 17:39 EDT 2019. Contains 328319 sequences. (Running on oeis4.)