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A208517 Triangle of coefficients of polynomials v(n,x) jointly generated with A208516; see the Formula section. 3
1, 1, 3, 1, 3, 7, 1, 3, 8, 17, 1, 3, 9, 22, 41, 1, 3, 10, 27, 59, 99, 1, 3, 11, 32, 78, 157, 239, 1, 3, 12, 37, 98, 222, 414, 577, 1, 3, 13, 42, 119, 294, 622, 1084, 1393, 1, 3, 14, 47, 141, 373, 864, 1722, 2821, 3363, 1, 3, 15, 52, 164, 459, 1141, 2500, 4719 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..64.

FORMULA

u(n,x)=u(n-1,x)+x*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...7

1...3...8...17

1...3...9...22...41

First five polynomials v(n,x):

1

1 + 3x

1 + 3x + 7x^2

1 + 3x + 8x^2 + 17x^3

1 + 3x + 9x^2 + 22x^3 + 41x^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] + 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[%]  (* A208516 *)

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

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

TableForm[cv]

Flatten[%]  (* A208517 *)

CROSSREFS

Cf. A208514.

Sequence in context: A257258 A259325 A094250 * A209566 A208916 A209766

Adjacent sequences:  A208514 A208515 A208516 * A208518 A208519 A208520

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 28 2012

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)