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A209759 Triangle of coefficients of polynomials u(n,x) jointly generated with A209760; see the Formula section. 3
1, 1, 2, 1, 5, 5, 1, 5, 16, 13, 1, 5, 19, 48, 34, 1, 5, 19, 68, 141, 89, 1, 5, 19, 71, 233, 409, 233, 1, 5, 19, 71, 262, 772, 1175, 610, 1, 5, 19, 71, 265, 948, 2492, 3349, 1597, 1, 5, 19, 71, 265, 986, 3354, 7879, 9482, 4181, 1, 5, 19, 71, 265, 989, 3641 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Limiting row: A001834

Coefficient of x^n in u(n,x):  odd-indexed Fibonacci numbers

Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...; A033999

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

LINKS

Table of n, a(n) for n=1..62.

FORMULA

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

v(n,x)=x*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

1...5...5

1...5...16...13

1...5...19...48...34

First three polynomials u(n,x): 1, 1 + 2x, 1 + 5x + 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*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[%]    (* A209759 *)

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

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

TableForm[cv]

Flatten[%]    (* A209760 *)

CROSSREFS

Cf. A209760, A208510.

Sequence in context: A300661 A145882 A209765 * A111785 A304462 A021468

Adjacent sequences:  A209756 A209757 A209758 * A209760 A209761 A209762

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 14 2012

STATUS

approved

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)