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A209820 Triangle of coefficients of polynomials v(n,x) jointly generated with A209819; see the Formula section. 3
1, 2, 2, 2, 6, 5, 2, 8, 18, 12, 2, 8, 30, 52, 29, 2, 8, 34, 104, 146, 70, 2, 8, 34, 136, 342, 402, 169, 2, 8, 34, 144, 514, 1080, 1090, 408, 2, 8, 34, 144, 594, 1848, 3306, 2920, 985, 2, 8, 34, 144, 610, 2360, 6370, 9872, 7746, 2378, 2, 8, 34, 144, 610, 2552 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let T(n,k) be the general term.

T(n,n): A000129

T(n,n-1): 2*A071667

Row sums: A003462

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

Limiting row: F(3), F(6),F(9),...where F=A000045 (Fibonacci numbers)

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

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

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

EXAMPLE

First five rows:

1

2...2

2...6...5

2...8...18...12

2...8...30...52...29

First three polynomials v(n,x): 1, 2 + 2x , 2 + 6x + 5x^2.

MATHEMATICA

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

u[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;

v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%]    (* A209819 *)

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

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

TableForm[cv]

Flatten[%]    (* A209820 *)

CROSSREFS

Cf. A209819, A208510.

Sequence in context: A309078 A241543 A210740 * A145890 A097091 A094204

Adjacent sequences:  A209817 A209818 A209819 * A209821 A209822 A209823

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 23 2012

STATUS

approved

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)