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A210220 Triangle of coefficients of polynomials v(n,x) jointly generated with A210217; see the Formula section. 4
1, 2, 2, 3, 6, 3, 4, 12, 13, 4, 5, 20, 34, 24, 5, 6, 30, 70, 80, 40, 6, 7, 42, 125, 200, 166, 62, 7, 8, 56, 203, 420, 496, 314, 91, 8, 9, 72, 308, 784, 1211, 1106, 553, 128, 9, 10, 90, 444, 1344, 2576, 3108, 2269, 920, 174, 10, 11, 110, 615, 2160, 4956, 7476 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First and last term in row n: n

Column 2: n*(n-1)

Column 3: A016061

Column 4: A112742

Row sums: -1+(even-indexed Fibonacci numbers)

Periodic alternating row sums: 1,0,0,1,0,0,1,0,0,...

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)+1,

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...6....3

4...12...13...4

5...20...34...24...5

First three polynomials v(n,x): 1, 2 + 2x , 3 + 6x + 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] + 1;

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[%]     (* A210219 *)

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

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

TableForm[cv]

Flatten[%]     (* A210220 *)

CROSSREFS

Cf. A210219, A208510.

Sequence in context: A047662 A183474 A294034 * A075196 A196912 A197079

Adjacent sequences:  A210217 A210218 A210219 * A210221 A210222 A210223

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 19 2012

STATUS

approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)