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A208608 Triangle of coefficients of polynomials u(n,x) jointly generated with A208609; see the Formula section. 3
1, 1, 1, 1, 3, 2, 1, 5, 6, 3, 1, 7, 12, 12, 5, 1, 9, 20, 29, 23, 8, 1, 11, 30, 56, 64, 43, 13, 1, 13, 42, 95, 140, 136, 79, 21, 1, 15, 56, 148, 265, 332, 279, 143, 34, 1, 17, 72, 217, 455, 692, 751, 558, 256, 55, 1, 19, 90, 304, 728, 1295, 1708, 1641, 1093, 454 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

coefficient of x^(n-1)=Fibonacci(n)=A000045(n)

LINKS

Table of n, a(n) for n=1..65.

FORMULA

u(n,x)=u(n-1,x)+x*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 five rows:

1

1...1

1...3...2

1...5...6....3

1...7...12...12...5

First five polynomials u(n,x):

1

1 + x

1 + 3x + 2x^2

1 + 5x + 6x^2 + 3x^3

1 + 7x + 12x^2 + 12x^3 + 5x^4

MATHEMATICA

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

u[n_, x_] := u[n - 1, x] + 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[%]  (* A208608 *)

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

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

TableForm[cv]

Flatten[%]  (* A208609 *)

CROSSREFS

Cf. A208609.

Sequence in context: A132969 A132970 A192022 * A209577 A139377 A110712

Adjacent sequences:  A208605 A208606 A208607 * A208609 A208610 A208611

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 29 2012

STATUS

approved

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Last modified November 28 06:47 EST 2014. Contains 250285 sequences.