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

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A207536 Triangle of coefficients of polynomials u(n,x) jointly generated with A105070; see Formula section. 3
1, 1, 2, 1, 6, 1, 12, 4, 1, 20, 20, 1, 30, 60, 8, 1, 42, 140, 56, 1, 56, 280, 224, 16, 1, 72, 504, 672, 144, 1, 90, 840, 1680, 720, 32, 1, 110, 1320, 3696, 2640, 352, 1, 132, 1980, 7392, 7920, 2112, 64, 1, 156, 2860, 13728, 20592, 9152, 832, 1, 182, 4004 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Subtriangle of the triangle given by (1, 0, 1, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 2, -2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Apr 08 2012

LINKS

Table of n, a(n) for n=1..58.

FORMULA

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

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

Contribution from Philippe Deléham, Apr 08 2012 . (Start)

As DELTA-triangle T(n,k) with 0<=k<=n :

G.f.: (1-x)/(1-2*x+x^2-2*y*x^2) .

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

T(n,k) = A034839(n,k)*2^k = binomial(n,2*k)*2^k . (End)

EXAMPLE

First seven rows:

1...

1...2

1...6

1...12...4

1...20...20

1...30...60...8

1...42...140..56

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

1

1, 0

1, 2, 0

1, 6, 0, 0

1, 12, 4, 0, 0

1, 20, 20, 0, 0, 0

1, 30, 60, 8, 0, 0, 0

1, 42, 140, 56, 0, 0, 0, 0 . - Philippe Deléham, Apr 08 2012

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_] := u[n - 1, x] + v[n - 1, x]

Table[Factor[u[n, x]], {n, 1, z}]

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

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]  (* A207536 *)

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

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

TableForm[cv]

Flatten[%]  (* A105070 *)

CROSSREFS

Cf. A105070.

Sequence in context: A139625 A053785 A233809 * A060173 A059344 A109193

Adjacent sequences:  A207533 A207534 A207535 * A207537 A207538 A207539

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 18 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 December 14 07:15 EST 2018. Contains 318090 sequences. (Running on oeis4.)