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A210599 Triangle of coefficients of polynomials v(n,x) jointly generated with A210221; see the Formula section. 3
1, 2, 3, 3, 8, 8, 4, 16, 28, 21, 5, 26, 69, 92, 55, 6, 39, 134, 268, 290, 144, 7, 54, 233, 606, 974, 888, 377, 8, 72, 368, 1196, 2510, 3378, 2662, 987, 9, 92, 550, 2122, 5541, 9760, 11313, 7852, 2584, 10, 115, 780, 3510, 10900, 23825, 36188, 36872 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with n and ends with an even-indexed Fibonacci number. For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..53.

FORMULA

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

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...3

3...8....8

4...16...28...21

5...26...69...92...55

First three polynomials v(n,x): 1, 2 + 3x, 3 + 8x + 8x^2

MATHEMATICA

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

u[n_, x_] := x*u[n - 1, x] + (x + 1)*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[%]    (* A210598 *)

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

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

TableForm[cv]

Flatten[%]    (* A210599 *)

CROSSREFS

Cf. A210598, A208510.

Sequence in context: A256679 A193997 A210752 * A211879 A308774 A308859

Adjacent sequences:  A210596 A210597 A210598 * A210600 A210601 A210602

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 24 2012

STATUS

approved

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Last modified October 22 03:04 EDT 2019. Contains 328315 sequences. (Running on oeis4.)