A208916 - OEIS

A208916

Triangle of coefficients of polynomials v(n,x) jointly generated with A208915; see the Formula section.

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

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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...3

1...3...7

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

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

First five polynomials v(n,x):

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: A208517 A336203 A209566 * A209766 A356207 A114972

Adjacent sequences: A208913 A208914 A208915 * A208917 A208918 A208919

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 03 2012

STATUS

approved