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A210227 Triangle of coefficients of polynomials u(n,x) jointly generated with A210228; see the Formula section. 2
1, 2, 1, 2, 6, 1, 2, 8, 16, 1, 2, 8, 32, 38, 1, 2, 8, 36, 112, 84, 1, 2, 8, 36, 156, 348, 178, 1, 2, 8, 36, 164, 620, 988, 368, 1, 2, 8, 36, 164, 732, 2244, 2624, 750, 1, 2, 8, 36, 164, 748, 3108, 7468, 6632, 1516, 1, 2, 8, 36, 164, 748, 3380, 12348, 23164 (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..63.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...1

2...6...1

2...8...16...1

2...8...32...38...1

First three polynomials u(n,x): 1, 2 + x, 2 + 6x + 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_] := 2 x*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[%]     (* A210225 *)

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

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

TableForm[cv]

Flatten[%]     (* A210226 *)

CROSSREFS

Cf. A210228, A208510.

Sequence in context: A129116 A096179 A166350 * A208757 A133643 A008305

Adjacent sequences:  A210224 A210225 A210226 * A210228 A210229 A210230

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 20 2012

STATUS

approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)