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A210218 Triangle of coefficients of polynomials v(n,x) jointly generated with A210217; see the Formula section. 3
1, 1, 3, 1, 4, 7, 1, 4, 13, 15, 1, 4, 14, 38, 31, 1, 4, 14, 47, 103, 63, 1, 4, 14, 48, 151, 264, 127, 1, 4, 14, 48, 163, 462, 649, 255, 1, 4, 14, 48, 164, 544, 1348, 1546, 511, 1, 4, 14, 48, 164, 559, 1768, 3769, 3595, 1023, 1, 4, 14, 48, 164, 560, 1893, 5564 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Limiting row:  A007070

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

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

EXAMPLE

First five rows:

1

1...3

1...4...7

1...4...13...15

1...4...14...38...31

First three polynomials v(n,x): 1, 1 + 3x , 1 + 4x + 7x^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*u[n - 1, x] + 2 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[%]    (* A210217 *)

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

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

TableForm[cv]

Flatten[%]    (* A210218 *)

CROSSREFS

Cf. A210217, A208510.

Sequence in context: A028861 A081521 A213224 * A086273 A054143 A104746

Adjacent sequences:  A210215 A210216 A210217 * A210219 A210220 A210221

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 19 2012

STATUS

approved

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Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)