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A208514 Triangle of coefficients of polynomials u(n,x) jointly generated with A208515; see the Formula section. 4
1, 1, 1, 1, 2, 2, 1, 3, 4, 3, 1, 4, 6, 7, 5, 1, 5, 8, 12, 13, 8, 1, 6, 10, 18, 24, 23, 13, 1, 7, 12, 25, 38, 46, 41, 21, 1, 8, 14, 33, 55, 78, 88, 72, 34, 1, 9, 16, 42, 75, 120, 158, 165, 126, 55, 1, 10, 18, 52, 98, 173, 255, 313, 307, 219, 89, 1, 11, 20, 63, 124, 238 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

u(n,n) = Fibonacci(n), A000054

u(n+1,n) = A208354(n)

col 1:  A000012

col 2:  A000027

col 3:  A005843

col 4:  A055998

col 5:  A140090

LINKS

Table of n, a(n) for n=1..72.

FORMULA

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

v(n,x)=x*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...2...2

1...3...4...3

1...4...6...7...5

First five polynomials u(n,x):

1

1 + x

1 + 2x + 2x^2

1 + 3x + 4x^2 + 3x^3

1 + 4x + 6x^2 + 7x^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*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[%]    (* A208514 *)

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

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

TableForm[cv]

Flatten[%]    (* A208515 *)

CROSSREFS

Cf. A208515.

Sequence in context: A323899 A182630 A208805 * A179901 A209561 A283822

Adjacent sequences:  A208511 A208512 A208513 * A208515 A208516 A208517

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 28 2012

STATUS

approved

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Last modified October 20 04:37 EDT 2019. Contains 328247 sequences. (Running on oeis4.)