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A209151 Triangle of coefficients of polynomials u(n,x) jointly generated with A208337; see the Formula section. 2
1, 2, 1, 3, 4, 2, 4, 8, 8, 3, 5, 13, 19, 15, 5, 6, 19, 36, 42, 28, 8, 7, 26, 60, 91, 89, 51, 13, 8, 34, 92, 170, 216, 182, 92, 21, 9, 43, 133, 288, 446, 489, 363, 164, 34, 10, 53, 184, 455, 826, 1105, 1068, 709, 290, 55, 11, 64, 246, 682, 1414, 2219, 2619 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Last term in each row is a Fibonacci number (A000045).

Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...

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

LINKS

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

FORMULA

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

v(n,x)=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

3...4....2

4...8....8....3

5...13...19...15...5

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

MATHEMATICA

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

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

v[n_, x_] := 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[%]    (* A209151 *)

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

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

TableForm[cv]

Flatten[%]    (* A208337 *)

CROSSREFS

Cf. A208337, A208510.

Sequence in context: A131389 A131394 A130585 * A125100 A128544 A120058

Adjacent sequences:  A209148 A209149 A209150 * A209152 A209153 A209154

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 07 2012

STATUS

approved

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)