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A209570 Triangle of coefficients of polynomials v(n,x) jointly generated with A209569; see the Formula section. 3
1, 2, 2, 3, 4, 2, 4, 8, 8, 2, 5, 14, 20, 12, 2, 6, 22, 42, 40, 16, 2, 7, 32, 78, 102, 68, 20, 2, 8, 44, 132, 222, 210, 104, 24, 2, 9, 58, 208, 432, 534, 382, 148, 28, 2, 10, 74, 310, 772, 1188, 1126, 634, 200, 32, 2, 11, 92, 442, 1290, 2392, 2848, 2142, 982 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For n>1, row n begins and ends with 2.

Alternating row sums:  1,0,1,2,1,0,1,2,1,0,1,2,...

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),

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

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

EXAMPLE

First five rows:

1

2...2

3...4....2

4...8....8....2

5...14...20...12...2

First three polynomials v(n,x): 1, 2 + 2x , 3 + 4x + 2x^2.

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];

v[n_, x_] := 2 x*u[n - 1, 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[%]   (* A209569 *)

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

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

TableForm[cv]

Flatten[%]   (* A209570 *)

CROSSREFS

Cf. A209569, A208510.

Sequence in context: A143595 A211702 A208521 * A205703 A325785 A207632

Adjacent sequences:  A209567 A209568 A209569 * A209571 A209572 A209573

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 10 2012

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)