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A209568 Triangle of coefficients of polynomials v(n,x) jointly generated with A209567; see the Formula section. 3
1, 2, 2, 3, 5, 3, 4, 10, 11, 4, 5, 17, 28, 21, 5, 6, 26, 58, 67, 36, 6, 7, 37, 105, 166, 142, 57, 7, 8, 50, 173, 350, 416, 274, 85, 8, 9, 65, 266, 659, 1011, 940, 491, 121, 9, 10, 82, 388, 1141, 2156, 2612, 1955, 829, 166, 10, 11, 101, 543, 1852, 4172, 6265 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n begins and ends with n.

Column 2: (n-1)^2, for n>1.

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

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

LINKS

Table of n, a(n) for n=1..61.

FORMULA

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

v(n,x)=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

2...2

3...5...3

4...10...11...4

5...17...28...21...5

First three polynomials v(n,x): 1, 2+2x, 3+5x+3x^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_] := 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[%]   (* A209567 *)

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

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

TableForm[cv]

Flatten[%]   (* A209568 *)

CROSSREFS

Cf. A209567, A208510.

Sequence in context: A210232 A047666 A285935 * A227641 A295097 A295551

Adjacent sequences:  A209565 A209566 A209567 * A209569 A209570 A209571

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 10 2012

STATUS

approved

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)