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A210223 Triangle of coefficients of polynomials u(n,x) jointly generated with A210224; see the Formula section. 3
1, 2, 1, 2, 5, 1, 2, 7, 10, 1, 2, 7, 22, 17, 1, 2, 7, 26, 57, 26, 1, 2, 7, 26, 89, 126, 37, 1, 2, 7, 26, 97, 266, 247, 50, 1, 2, 7, 26, 97, 346, 695, 442, 65, 1, 2, 7, 26, 97, 362, 1127, 1618, 737, 82, 1, 2, 7, 26, 97, 362, 1319, 3298, 3425, 1162, 101, 1, 2, 7, 26 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Limiting row:  A001075

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

LINKS

Table of n, a(n) for n=1..69.

FORMULA

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

v(n,x)=2x*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

2...5...1

2...7...10...1

2...7...22...17...1

First three polynomials u(n,x): 1, 2 + x, 2 + 5x + 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*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[%]     (* A210223 *)

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

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

TableForm[cv]

Flatten[%]     (* A210224 *)

CROSSREFS

Cf. A210224, A208510.

Sequence in context: A144224 A122881 A210217 * A242598 A225568 A291694

Adjacent sequences:  A210220 A210221 A210222 * A210224 A210225 A210226

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 20 2012

STATUS

approved

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Last modified October 17 18:58 EDT 2019. Contains 328127 sequences. (Running on oeis4.)