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A209762 Triangle of coefficients of polynomials v(n,x) jointly generated with A209761; see the Formula section. 3
1, 2, 2, 3, 5, 4, 4, 10, 14, 8, 5, 17, 34, 36, 16, 6, 26, 68, 104, 88, 32, 7, 37, 120, 240, 296, 208, 64, 8, 50, 194, 480, 776, 800, 480, 128, 9, 65, 294, 868, 1736, 2352, 2080, 1088, 256, 10, 82, 424, 1456, 3472, 5824, 6784, 5248, 2432, 512, 11, 101, 588 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 1: 1,2,3,4,5,6,7,8,...

Column 2: 1+1, 1+2^2, 1+3^2, 1+4^2,...

Last term in row n:  2^(n-1)

Alternating row sums: 1,0,2,0,2,0,2,0,2,0,2,0,...

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

LINKS

Table of n, a(n) for n=1..58.

FORMULA

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

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

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First five rows:

1

2...2

3...5....4

4...10...14...8

5...17...34...36...16

First three polynomials v(n,x): 1, 2 + 2x , 3 + 5x + 4x^2.

MATHEMATICA

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

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

v[n_, x_] := x*u[n - 1, x] + (x + 1)*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[%]    (* A209761 *)

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

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

TableForm[cv]

Flatten[%]    (* A209762 *)

CROSSREFS

Cf. A209761, A208510.

Sequence in context: A210554 A208912 A210212 * A026408 A209147 A036716

Adjacent sequences:  A209759 A209760 A209761 * A209763 A209764 A209765

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 14 2012

STATUS

approved

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Last modified April 25 00:50 EDT 2014. Contains 240991 sequences.