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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A210755 Triangle of coefficients of polynomials u(n,x) jointly generated with A210756; see the Formula section. 3
1, 2, 3, 3, 11, 7, 4, 26, 38, 17, 5, 50, 124, 121, 41, 6, 85, 314, 499, 362, 99, 7, 133, 679, 1555, 1805, 1043, 239, 8, 196, 1316, 4054, 6672, 6096, 2926, 577, 9, 276, 2352, 9318, 20326, 26048, 19610, 8049, 1393, 10, 375, 3948, 19482, 53932, 90706 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with n and ends with A001333(n).

Column 2: A051925

Row sums: A002450

Alternating row sums: 1,-1,-1,-1,-1,-1,...

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

LINKS

Table of n, a(n) for n=1..51.

FORMULA

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

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

2...3

3...11...7

4...26...38....17

5...50...124...121...41

First three polynomials u(n,x): 1, 2 + 3x, 3 + 11x + 7x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*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[%]    (* A210755 *)

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

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

TableForm[cv]

Flatten[%]    (* A210756 *)

Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A002450 *)

Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A002450 *)

CROSSREFS

Cf. A210754, A208510.

Sequence in context: A155758 A009097 A210194 * A219224 A265532 A112858

Adjacent sequences:  A210752 A210753 A210754 * A210756 A210757 A210758

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 25 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 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)