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A210751 Triangle of coefficients of polynomials u(n,x) jointly generated with A210752; see the Formula section. 3
1, 2, 2, 3, 6, 5, 4, 12, 19, 13, 5, 20, 46, 59, 34, 6, 30, 90, 166, 179, 89, 7, 42, 155, 370, 572, 533, 233, 8, 56, 245, 715, 1426, 1904, 1564, 610, 9, 72, 364, 1253, 3046, 5240, 6171, 4536, 1597, 10, 90, 516, 2044, 5845, 12237, 18561, 19581, 13031 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with n and ends with F(2n-1), where F=A000045 (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+1)*u(n-1,x)+x*v(n-1,x)+1,

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

2...2

3...6....5

4...12...19...13

5...20...46...59...34

First three polynomials u(n,x): 1, 2 + 2x, 3 + 6x + 5x^2.

MATHEMATICA

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

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

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[%]    (* A210751 *)

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

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

TableForm[cv]

Flatten[%]    (* A210752 *)

CROSSREFS

Cf. A210752, A208510.

Sequence in context: A207623 A116447 A137757 * A279791 A132886 A119272

Adjacent sequences:  A210748 A210749 A210750 * A210752 A210753 A210754

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 25 2012

STATUS

approved

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Last modified October 23 14:45 EDT 2019. Contains 328345 sequences. (Running on oeis4.)