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A209706 Triangle of coefficients of polynomials v(n,x) jointly generated with A209705; see the Formula section. 3
1, 3, 2, 4, 7, 4, 5, 14, 18, 8, 6, 23, 46, 44, 16, 7, 34, 92, 136, 104, 32, 8, 47, 160, 320, 376, 240, 64, 9, 62, 254, 640, 1016, 992, 544, 128, 10, 79, 378, 1148, 2296, 3024, 2528, 1216, 256, 11, 98, 536, 1904, 4592, 7616, 8576, 6272, 2688, 512, 12, 119 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,...

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

LINKS

Table of n, a(n) for n=1..57.

FORMULA

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

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

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

T(n,k) = 2*T(n-1,k)+2*T(n-1,k-1)-T(n-2,k)-2*T(n-2,k-1), T(1,0)=1, T(2,0)=3, T(2,1)=2, T(3,0)=4, T(3,1)=7, T(3,2)=4, T(n,k)=0 if k<0 or if k>=n. - Philippe Deléham, Dec 27 2013

EXAMPLE

First five rows:

1

3...2

4...7....4

5...14...18...8

6...23...46...44...16

First three polynomials v(n,x): 1, 3 + 2x , 4 + 7x + 4x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*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[%]  (* A209705 *)

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

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

TableForm[cv]

Flatten[%]  (* A209706 *)

CROSSREFS

Cf. A209705, A208510.

Sequence in context: A317736 A060006 A123097 * A134571 A054086 A163329

Adjacent sequences:  A209703 A209704 A209705 * A209707 A209708 A209709

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved

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Last modified October 23 07:05 EDT 2019. Contains 328335 sequences. (Running on oeis4.)