A208511 - OEIS

A208511

Triangle of coefficients of polynomials u(n,x) jointly generated with A208512; see the Formula section.

1, 1, 1, 1, 3, 2, 1, 5, 7, 4, 1, 7, 14, 16, 8, 1, 9, 23, 37, 36, 16, 1, 11, 34, 69, 94, 80, 32, 1, 13, 47, 114, 195, 232, 176, 64, 1, 15, 62, 174, 354, 528, 560, 384, 128, 1, 17, 79, 251, 588, 1041, 1384, 1328, 832, 256, 1, 19, 98, 347, 916, 1863, 2938, 3536

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OFFSET

1,5

LINKS

Table of n, a(n) for n=1..63.

FORMULA

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

v(n,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

1...3...2

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

1...7...14...16...8

First five polynomials u(n,x):

1 + x

1 + 3x + 2x^2

1 + 5x + 7x^2 + 4x^3

1 + 7x + 14x^2 + 16x^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_] := 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[%] (* A208511 *)

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

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

TableForm[cv]

Flatten[%] (* A208512 *)

CROSSREFS

Cf. A208511.

Sequence in context: A360364 A092879 A073370 * A129675 A232206 A209559

Adjacent sequences: A208508 A208509 A208510 * A208512 A208513 A208514

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 28 2012

STATUS

approved