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A209688 Triangle of coefficients of polynomials v(n,x) jointly generated with A115241; see the Formula section. 2
1, 3, 4, 2, 5, 5, 2, 6, 9, 7, 2, 7, 14, 16, 9, 2, 8, 20, 30, 25, 11, 2, 9, 27, 50, 55, 36, 13, 2, 10, 35, 77, 105, 91, 49, 15, 2, 11, 44, 112, 182, 196, 140, 64, 17, 2, 12, 54, 156, 294, 378, 336, 204, 81, 19, 2, 13, 65, 210, 450, 672, 714, 540, 285, 100, 21, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 1,3,2,2,2,2,2,2,2,2,2,2,...

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

LINKS

Table of n, a(n) for n=1..67.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

3...1

4...2...3

5...5...2

6...9...7...2

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

MATHEMATICA

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

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

v[n_, 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[%]    (* A115241 *)

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

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

TableForm[cv]

Flatten[%]   (* A209688 *)

CROSSREFS

Cf. A115241, A208510.

Sequence in context: A246832 A133570 A117041 * A143939 A197269 A201905

Adjacent sequences:  A209685 A209686 A209687 * A209689 A209690 A209691

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved

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Last modified November 21 14:18 EST 2019. Contains 329371 sequences. (Running on oeis4.)