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A210214 Triangle of coefficients of polynomials v(n,x) jointly generated with A210213; see the Formula section. 3
1, 3, 1, 6, 5, 1, 11, 14, 7, 1, 19, 34, 25, 9, 1, 32, 74, 75, 39, 11, 1, 53, 152, 195, 139, 56, 13, 1, 87, 299, 468, 419, 231, 76, 15, 1, 142, 571, 1056, 1147, 791, 356, 99, 17, 1, 231, 1066, 2280, 2911, 2429, 1364, 519, 125, 19, 1, 375, 1956, 4755, 6991 (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..59.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

3....1

6....5....1

11...14...7....1

19...34...25...9...1

First three polynomials v(n,x): 1, 3 + x , 6 + 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_] := 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[%]    (* A210213 *)

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

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

TableForm[cv]

Flatten[%]    (* A210214 *)

CROSSREFS

Cf. A210213, A208510.

Sequence in context: A109954 A153641 A133545 * A209149 A210602 A210801

Adjacent sequences:  A210211 A210212 A210213 * A210215 A210216 A210217

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 19 2012

STATUS

approved

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Last modified June 19 17:22 EDT 2018. Contains 305594 sequences. (Running on oeis4.)