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A209140 Triangle of coefficients of polynomials v(n,x) jointly generated with A209139; see the Formula section. 3
1, 1, 3, 2, 5, 7, 3, 12, 18, 17, 5, 23, 51, 58, 41, 8, 45, 118, 189, 175, 99, 13, 84, 264, 506, 645, 507, 239, 21, 155, 558, 1268, 1950, 2085, 1428, 577, 34, 281, 1145, 2974, 5395, 6998, 6482, 3940, 1393, 55, 504, 2286, 6687, 13851, 21141, 23856 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

column 1:  Fibonacci numbers, A000045

alternating row sums: (-2)^(n-1)

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

LINKS

Table of n, a(n) for n=1..52.

FORMULA

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

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

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

T(n,k) = T(n-1,k) + 2*T(n-1,k-1) + T(n-2,k) + T(n-2,k-2), T(1,0) = T(2,0) = 1, T(2,1) = 3, T(n,k) = 0 if k<0 or if k>=n.- Philippe Deléham, Apr 11 2012

EXAMPLE

First five rows:

1

1...3

2...5....7

3...12...18...17

5...23...51...58...41

First three polynomials v(n,x): 1, 1 + 3x, 2 + 5x + 7x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x];

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[%]    (* A209139 *)

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

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

TableForm[cv]

Flatten[%]    (* A209140 *)

CROSSREFS

Cf. A209139, A208510.

Sequence in context: A130295 A208613 A209584 * A265903 A006369 A097284

Adjacent sequences:  A209137 A209138 A209139 * A209141 A209142 A209143

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 05 2012

STATUS

approved

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Last modified August 20 01:14 EDT 2019. Contains 326136 sequences. (Running on oeis4.)