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A210878 Triangle of coefficients of polynomials u(n,x) jointly generated with A210879; see the Formula section. 3
1, 0, 3, 0, 4, 7, 0, 2, 14, 17, 0, 2, 12, 46, 41, 0, 2, 8, 54, 140, 99, 0, 2, 8, 42, 212, 408, 239, 0, 2, 8, 34, 200, 758, 1154, 577, 0, 2, 8, 34, 160, 866, 2544, 3194, 1393, 0, 2, 8, 34, 144, 754, 3448, 8154, 8696, 3363, 0, 2, 8, 34, 144, 642, 3400, 12850 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Leading coefficient of u(n,x):  A001333

Limiting row:  0,2,8,34,144,610,...(Fibonacci numbers)

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

LINKS

Table of n, a(n) for n=1..63.

FORMULA

u(n,x)=x*u(n-1,x)+2x*v(n-1,x),

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

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

EXAMPLE

First six rows:

1

0...3

0...4...7

0...2...14...17

0...2...12...46...41

0...2...8....54...140...99

First three polynomials u(n,x): 1, 3x, 4x + 7x^2.

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 14;

u[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x];

v[n_, x_] := (x + 1)*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[%]    (* A210878 *)

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

TableForm[cv]

Flatten[%]    (* A210879 *)

CROSSREFS

Cf. A210879, A208510.

Sequence in context: A111493 A190181 A145092 * A320373 A303274 A199608

Adjacent sequences:  A210875 A210876 A210877 * A210879 A210880 A210881

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 30 2012

STATUS

approved

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Last modified December 1 07:59 EST 2021. Contains 349426 sequences. (Running on oeis4.)