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A209694 Triangle of coefficients of polynomials v(n,x) jointly generated with A209693; see the Formula section. 3
1, 3, 1, 4, 6, 1, 5, 13, 10, 1, 6, 22, 32, 15, 1, 7, 33, 71, 66, 21, 1, 8, 46, 131, 186, 121, 28, 1, 9, 61, 216, 415, 422, 204, 36, 1, 10, 78, 330, 801, 1121, 862, 323, 45, 1, 11, 97, 477, 1400, 2507, 2689, 1625, 487, 55, 1, 12, 118, 661, 2276, 4977, 6902 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums are periodic.  For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..61.

FORMULA

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

v(n,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

3...1

4...6....1

5...13...10...1

6...22...32...15...1

First three polynomials v(n,x): 1, 3 + x , 4 + 6x + x^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_] := 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[%]   (* A209693 *)

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

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

TableForm[cv]

Flatten[%]   (* A209694 *)

CROSSREFS

Cf. A209693, A208510.

Sequence in context: A209518 A108285 A207619 * A286951 A260355 A075419

Adjacent sequences:  A209691 A209692 A209693 * A209695 A209696 A209697

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved

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Last modified October 20 05:42 EDT 2019. Contains 328247 sequences. (Running on oeis4.)