login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208755 Triangle of coefficients of polynomials u(n,x) jointly generated with A208756; see the Formula section. 4
1, 1, 2, 1, 2, 4, 1, 2, 6, 8, 1, 2, 8, 14, 16, 1, 2, 10, 20, 34, 32, 1, 2, 12, 26, 56, 78, 64, 1, 2, 14, 32, 82, 140, 178, 128, 1, 2, 16, 38, 112, 218, 352, 398, 256, 1, 2, 18, 44, 146, 312, 594, 852, 882, 512, 1, 2, 20, 50, 184, 422, 912, 1530, 2040, 1934, 1024 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

Subtriangle of the triangle given by (1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.- Philippe Deléham, Mar 05 2012

LINKS

Table of n, a(n) for n=1..66.

FORMULA

u(n,x)=u(n-1,x)+2x*v(n-1,x),

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

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

Contribution from Philippe Deléham, Mar 05 2012. (Start)

T(n,k) = T(n-1,k) + T(n-1,k-1) - T(n-2,k-1) + 2*T(n-2,k-2), T(1,0) = 1, T(2,0) = 1, T(2,1) = 1 and T(n,k) = 0 if k<0 or if k>n. (End)

G.f.: -(1+x*y)*x*y/(-1+x*y-x^2*y+2*x^2*y^2+x). - R. J. Mathar, Aug 11 2015

EXAMPLE

First five rows:

1

1...2

1...2...4

1...2...6...8

1...2...8...14...16

First five polynomials u(n,x):

1

1 + 2x

1 + 2x + 4x^2

1 + 2x + 6x^2 + 8x^3

1 + 2x + 8x^2 + 14x^3 + 16x^4

Triangle (1, 0, -1, 1, 0, 0, 0...) DELTA (0, 2, 0, -1, 0, 0, 0, ...) begins :

1

1, 0

1, 2, 0

1, 2, 4, 0

1, 2, 6, 8, 0

1, 2, 8, 14, 16, 0

1, 2, 10, 20, 34, 32, 0

MATHEMATICA

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

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

v[n_, x_] := x*u[n - 1, x] + 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[%]    (* A208755 *)

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

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

TableForm[cv]

Flatten[%]    (* A208756 *)

CROSSREFS

Cf. A208756, A208510.

Sequence in context: A203647 A114791 A129994 * A226441 A080246 A113413

Adjacent sequences:  A208752 A208753 A208754 * A208756 A208757 A208758

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 01 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 18 07:19 EDT 2019. Contains 328146 sequences. (Running on oeis4.)