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A209773 Triangle of coefficients of polynomials u(n,x) jointly generated with A209774; see the Formula section. 4
1, 1, 2, 2, 6, 5, 2, 11, 21, 13, 3, 17, 48, 67, 34, 3, 25, 92, 188, 206, 89, 4, 33, 154, 422, 684, 619, 233, 4, 44, 238, 809, 1756, 2365, 1829, 610, 5, 54, 348, 1411, 3801, 6833, 7882, 5334, 1597, 5, 68, 484, 2285, 7369, 16471, 25302, 25549, 15393 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Last term in row n: F(2n+1), where F=A000045, the Fibonacci numbers

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

LINKS

Table of n, a(n) for n=1..54.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...2

2...6....5

2...11...21...13

3...17...48...67...34

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

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*u[n - 1, x] + 2 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[%]    (* A209773 *)

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

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

TableForm[cv]

Flatten[%]    (* A209774 *)

CROSSREFS

Cf. A209774, A208510.

Sequence in context: A062400 A064766 A019749 * A209767 A122070 A181661

Adjacent sequences:  A209770 A209771 A209772 * A209774 A209775 A209776

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 15 2012

STATUS

approved

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Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)