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A209693 Triangle of coefficients of polynomials u(n,x) jointly generated with A209694; see the Formula section. 3
1, 0, 2, 0, 3, 3, 0, 4, 9, 4, 0, 5, 17, 19, 5, 0, 6, 27, 49, 34, 6, 0, 7, 39, 98, 115, 55, 7, 0, 8, 53, 170, 284, 236, 83, 8, 0, 9, 69, 269, 585, 706, 440, 119, 9, 0, 10, 87, 399, 1070, 1706, 1568, 763, 164, 10, 0, 11, 107, 564, 1799, 3577, 4395, 3193, 1250, 219 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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..65.

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

0...2

0...2...4

0...1...8...8

0...1...5...24...16

First three polynomials v(n,x): 1, 2x, 2x + 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_] := 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. A209694, A208510.

Sequence in context: A279587 A127952 A171307 * A154344 A134409 A327878

Adjacent sequences:  A209690 A209691 A209692 * A209694 A209695 A209696

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved

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Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)