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A210601 Triangle of coefficients of polynomials v(n,x) jointly generated with A210600; see the Formula section. 3
1, 3, 2, 6, 9, 4, 11, 26, 24, 8, 19, 63, 89, 60, 16, 32, 138, 265, 270, 144, 32, 53, 284, 693, 949, 760, 336, 64, 87, 560, 1664, 2870, 3072, 2032, 768, 128, 142, 1071, 3761, 7840, 10521, 9272, 5232, 1728, 256, 231, 2002, 8127, 19896, 32143, 35418 (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..51.

FORMULA

u(n,x)=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

3....2

6....9....4

11...26...24...8

19...63...89...60...16

First three polynomials v(n,x): 1, 3 + 2x, 6 + 9x + 4x^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] + (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[%]    (* A210600 *)

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

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

TableForm[cv]

Flatten[%]    (* A210601 *)

CROSSREFS

Cf. A210600, A208510.

Sequence in context: A318049 A210754 A210738 * A197493 A300070 A171632

Adjacent sequences:  A210598 A210599 A210600 * A210602 A210603 A210604

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 24 2012

STATUS

approved

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Last modified October 16 08:50 EDT 2019. Contains 328056 sequences. (Running on oeis4.)