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A210198 Triangle of coefficients of polynomials v(n,x) jointly generated with A210197; see the Formula section. 3
1, 3, 1, 7, 4, 15, 12, 1, 31, 32, 6, 63, 80, 24, 1, 127, 192, 80, 8, 255, 448, 240, 40, 1, 511, 1024, 672, 160, 10, 1023, 2304, 1792, 560, 60, 1, 2047, 5120, 4608, 1792, 280, 12, 4095, 11264, 11520, 5376, 1120, 84, 1, 8191, 24576, 28160, 15360, 4032 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums:  A005409

Column 1:  -1+2^n

Alternating row sums: 1, 2,3,4,5,6,..., A000027

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

LINKS

Table of n, a(n) for n=1..53.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

3....1

15...12...1

31...32...6

63...80...24...1

First three polynomials v(n,x): 1, 3 + x , 15 + 12x + x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%]   (* A210197 *)

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

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

TableForm[cv]

Flatten[%]  (* A210198 *)

Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A048739 *)

Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A005409 *)

Table[u[n, x] /. x -> -1, {n, 1, z}] (* A000217 *)

Table[v[n, x] /. x -> -1, {n, 1, z}] (* A000027 *)

CROSSREFS

Cf. A210197, A208510.

Sequence in context: A283764 A010603 A269423 * A271258 A100584 A185877

Adjacent sequences:  A210195 A210196 A210197 * A210199 A210200 A210201

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 18 2012

STATUS

approved

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Last modified October 14 04:35 EDT 2019. Contains 327995 sequences. (Running on oeis4.)