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A208515 Triangle of coefficients of polynomials v(n,x) jointly generated with A208514; see the Formula section. 3
1, 1, 2, 1, 2, 3, 1, 2, 4, 5, 1, 2, 5, 8, 8, 1, 2, 6, 11, 15, 13, 1, 2, 7, 14, 23, 28, 21, 1, 2, 8, 17, 32, 47, 51, 34, 1, 2, 9, 20, 42, 70, 93, 92, 55, 1, 2, 10, 23, 53, 97, 148, 181, 164, 89, 1, 2, 11, 26, 65, 128, 217, 306, 346, 290, 144, 1, 2, 12, 29, 78, 163, 301 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..73.

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...2

1...2...3

1...2...4...5

1...2...5...8...8

First five polynomials v(n,x):

1

1 + 2x

1 + 2x + 3x^2

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

1 + 2x + 5x^2 + 8x^3 + 8x^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. A208514.

Sequence in context: A209435 A263744 A268956 * A286880 A178030 A131879

Adjacent sequences:  A208512 A208513 A208514 * A208516 A208517 A208518

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 28 2012

STATUS

approved

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)