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A208918 Triangle of coefficients of polynomials v(n,x) jointly generated with A208917; see the Formula section. 3
1, 1, 4, 1, 4, 12, 1, 4, 16, 40, 1, 4, 20, 64, 128, 1, 4, 24, 88, 240, 416, 1, 4, 28, 112, 368, 896, 1344, 1, 4, 32, 136, 512, 1504, 3264, 4352, 1, 4, 36, 160, 672, 2240, 5952, 11776, 14080, 1, 4, 40, 184, 848, 3104, 9472, 23168, 41984, 45568, 1, 4, 44 (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..58.

FORMULA

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

v(n,x)=2x*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...4

1...4...12

1...4...16...40

1...4...20...64...128

First five polynomials v(n,x):

1

1 + 4x

1 + 4x + 12x^2

1 + 4x + 16x^2 + 40x^3

1 + 4x + 20x^2 + 64x^3 + 128x^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] + 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[%]    (* A208917 *)

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

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

TableForm[cv]

Flatten[%]    (* A208918 *)

CROSSREFS

Cf. A208917, A208510.

Sequence in context: A209576 A055886 A132478 * A228782 A205125 A248978

Adjacent sequences:  A208915 A208916 A208917 * A208919 A208920 A208921

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 04 2012

STATUS

approved

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Last modified October 22 11:06 EDT 2019. Contains 328318 sequences. (Running on oeis4.)