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A209746 Triangle of coefficients of polynomials v(n,x) jointly generated with A209745; see the Formula section. 3
1, 2, 2, 3, 7, 4, 5, 17, 20, 8, 8, 37, 65, 52, 16, 13, 75, 176, 210, 128, 32, 21, 146, 428, 679, 616, 304, 64, 34, 276, 971, 1921, 2312, 1696, 704, 128, 55, 511, 2097, 4970, 7449, 7240, 4464, 1600, 256, 89, 931, 4366, 12056, 21622, 26146, 21344 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n begins with F(n+1) and ends with 2^(n-1), where F=A000045 (Fibonacci numbers)

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

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

Riordan array ((1+x)/(1-x-x^2), (2x+x^2)/(1-x-x^2)). - Philippe Deléham, Mar 24 2012

Triangle given by (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 26 2012

LINKS

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

FORMULA

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

v(n,x)=(x+1)*u(n-1,x)+(x+1)*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-1), T(1,0) = 1, T(2,0) = T(2,1) = 2, T(n,k) = 0 if k<0 or if k>=0 . - Philippe Deléham, Mar 24 2012

EXAMPLE

First five rows:

1

2...2

3...7....4

5...17...20...8

8...37...65...52...16

First three polynomials v(n,x): 1, 2 + 2x , 3 + 7x + 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 + 1)*u[n - 1, x] + (x + 1)*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[%]    (* A209745 *)

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

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

TableForm[cv]

Flatten[%]    (* A209746 *)

CROSSREFS

Cf. A000045, A000079, A209745, A208510.

Sequence in context: A222894 A210753 A208762 * A267822 A210598 A051301

Adjacent sequences:  A209743 A209744 A209745 * A209747 A209748 A209749

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 13 2012

STATUS

approved

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Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)