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A209760 Triangle of coefficients of polynomials v(n,x) jointly generated with A209759; see the Formula section. 3
1, 1, 3, 1, 3, 8, 1, 3, 11, 21, 1, 3, 11, 38, 55, 1, 3, 11, 41, 124, 144, 1, 3, 11, 41, 150, 389, 377, 1, 3, 11, 41, 153, 533, 1187, 987, 1, 3, 11, 41, 153, 568, 1838, 3549, 2584, 1, 3, 11, 41, 153, 571, 2084, 6168, 10447, 6765, 1, 3, 11, 41, 153, 571, 2128 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Limiting row: A001835

Coefficient of x^n in v(n,x):  even-indexed Fibonacci numbers

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

LINKS

Table of n, a(n) for n=1..62.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...3

1...3...8

1...3...11...21

1...3...11...38...55

First three polynomials v(n,x): 1, 1 + 3x , 1 + 3x + 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];

v[n_, x_] := x*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[%]    (* A209759 *)

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

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

TableForm[cv]

Flatten[%]    (* A209760 *)

CROSSREFS

Cf. A208510.

Sequence in context: A132476 A103279 A208910 * A046544 A011088 A276228

Adjacent sequences:  A209757 A209758 A209759 * A209761 A209762 A209763

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 14 2012

STATUS

approved

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Last modified October 16 02:52 EDT 2019. Contains 328038 sequences. (Running on oeis4.)