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A208519 Triangle of coefficients of polynomials v(n,x) jointly generated with A208518; see the Formula section. 3
1, 2, 2, 3, 5, 3, 4, 9, 11, 5, 5, 14, 26, 23, 8, 6, 20, 50, 65, 45, 13, 7, 27, 85, 145, 150, 86, 21, 8, 35, 133, 280, 385, 329, 160, 34, 9, 44, 196, 490, 840, 952, 692, 293, 55, 10, 54, 276, 798, 1638, 2310, 2232, 1413, 529, 89, 11, 65, 375, 1230, 2940, 4956 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

coefficient of x^(n-1): Fibonacci(n+1) = A000045(n+1)

col 1:  A000027

col 2:  A000096

col 3:  A051925

row sums:  A002878 (bisection of Lucas sequence)

alternating row sums:  A000045(n-2), Fibonacci numbers

LINKS

Table of n, a(n) for n=1..61.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...2

3...5....3

4...9....11...5

5...14...26...23...8

First five polynomials v(n,x):

1

2 + 2x

3 + 5x + 3x^2

4 + 9x + 11x^2 + 5x^3

5 + 14x + 26x^2 + 23x^3 + 8x^4

MATHEMATICA

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

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

v[n_, x_] := x*u[n - 1, x] + (x + 1)*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[%]   (* A208518 *)

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

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

TableForm[cv]

Flatten[%]   (* A208519 *)

CROSSREFS

Cf. A208518.

Sequence in context: A124727 A210565 A125101 * A210232 A047666 A285935

Adjacent sequences:  A208516 A208517 A208518 * A208520 A208521 A208522

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 28 2012

STATUS

approved

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Last modified October 23 05:56 EDT 2019. Contains 328335 sequences. (Running on oeis4.)