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A209556 Triangle of coefficients of polynomials v(n,x) jointly generated with A209555; see the Formula section. 3
1, 2, 1, 2, 3, 1, 3, 4, 4, 1, 3, 8, 7, 5, 1, 4, 9, 17, 11, 6, 1, 4, 15, 22, 31, 16, 7, 1, 5, 16, 43, 46, 51, 22, 8, 1, 5, 24, 50, 102, 86, 78, 29, 9, 1, 6, 25, 86, 130, 212, 148, 113, 37, 10, 1, 6, 35, 95, 250, 296, 400, 239, 157, 46, 11, 1, 7, 36, 150, 295, 626, 610 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..72.

FORMULA

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

v(n,x)=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...1

2...3...1

3...4...4...1

3...8...7...5...1

First three polynomials v(n,x): 1, 2 + x , 2+ 3x + x^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_] := 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[%]    (* A209555 *)

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

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

TableForm[cv]

Flatten[%]    (* A209556 *)

CROSSREFS

Cf. A209555, A208510.

Sequence in context: A080786 A036838 A066010 * A109974 A213008 A215520

Adjacent sequences:  A209553 A209554 A209555 * A209557 A209558 A209559

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 10 2012

STATUS

approved

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Last modified October 17 16:41 EDT 2019. Contains 328120 sequences. (Running on oeis4.)