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A210235 Triangle of coefficients of polynomials u(n,x) jointly generated with A210236; see the Formula section. 4
1, 2, 1, 4, 4, 1, 7, 12, 7, 1, 12, 29, 28, 11, 1, 20, 64, 86, 56, 16, 1, 33, 132, 230, 210, 101, 22, 1, 54, 261, 560, 662, 451, 169, 29, 1, 88, 500, 1279, 1860, 1646, 883, 267, 37, 1, 143, 936, 2785, 4819, 5257, 3682, 1611, 403, 46, 1, 232, 1721, 5848 (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..58.

FORMULA

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

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

2....1

4....4....1

7....12...7....1

12...29...28...11...1

First three polynomials u(n,x): 1, 2 + x, 4 + 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 + 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[%]      (* A210235 *)

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

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

TableForm[cv]

Flatten[%]      (* A210236 *)

CROSSREFS

Cf. A210236, A208510.

Sequence in context: A209145 A214984 A118976 * A138177 A101559 A220537

Adjacent sequences:  A210232 A210233 A210234 * A210236 A210237 A210238

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 20 2012

STATUS

approved

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Last modified October 19 03:24 EDT 2019. Contains 328211 sequences. (Running on oeis4.)