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A208916 Triangle of coefficients of polynomials v(n,x) jointly generated with A208915; see the Formula section. 3
1, 1, 3, 1, 3, 7, 1, 3, 11, 19, 1, 3, 15, 35, 47, 1, 3, 19, 51, 107, 123, 1, 3, 23, 67, 183, 323, 311, 1, 3, 27, 83, 275, 603, 939, 803, 1, 3, 31, 99, 383, 963, 1951, 2723, 2047, 1, 3, 35, 115, 507, 1403, 3411, 6147, 7723, 5259, 1, 3, 39, 131, 647, 1923, 5383 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

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

FORMULA

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

v(n,x)=2x*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...3

1...3...7

1...3...11...19

1...3...15...35...47

First five polynomials v(n,x):

1

1 + 3x

1 + 3x + 7x^2

1 + 3x + 11x^2 + 19x^3

1 + 3x + 15x^2 + 35x^3 + 47x^4

MATHEMATICA

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

u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];

v[n_, x_] := 2 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[%]    (* A208915 *)

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

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

TableForm[cv]

Flatten[%]    (* A208916 *)

CROSSREFS

Cf. A208915, A208510.

Sequence in context: A094250 A208517 A209566 * A209766 A114972 A107461

Adjacent sequences:  A208913 A208914 A208915 * A208917 A208918 A208919

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 03 2012

STATUS

approved

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Last modified October 22 00:52 EDT 2019. Contains 328315 sequences. (Running on oeis4.)