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A209170 Triangle of coefficients of polynomials u(n,x) jointly generated with A209171; see the Formula section. 3
1, 2, 1, 5, 6, 2, 11, 20, 13, 3, 23, 57, 57, 27, 5, 47, 149, 202, 144, 53, 8, 95, 369, 633, 604, 334, 101, 13, 191, 881, 1831, 2192, 1618, 733, 188, 21, 383, 2049, 5007, 7217, 6665, 4022, 1544, 344, 34, 767, 4673, 13135, 22153, 24570, 18519, 9461 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n ends with A000045 (Fibonacci numbers).

Alternating row sums: 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..52.

FORMULA

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

v(n,x)=(x+1)*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....1

5....6....2

11...20...13...3

23...57...57...27...5

First three polynomials v(n,x): 1, 2 + x, 5 + 6x + 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 + 1)*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[%]    (* A209170 *)

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

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

TableForm[cv]

Flatten[%]    (* A209171 *)

CROSSREFS

Cf. A209171, A208510.

Sequence in context: A078123 A323312 A231774 * A231732 A185384 A274728

Adjacent sequences:  A209167 A209168 A209169 * A209171 A209172 A209173

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 08 2012

STATUS

approved

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