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A210204 Triangle of coefficients of polynomials v(n,x) jointly generated with A210203; see the Formula section. 4
1, 3, 2, 7, 8, 2, 15, 24, 12, 2, 31, 64, 48, 16, 2, 63, 160, 160, 80, 20, 2, 127, 384, 480, 320, 120, 24, 2, 255, 896, 1344, 1120, 560, 168, 28, 2, 511, 2048, 3584, 3584, 2240, 896, 224, 32, 2, 1023, 4608, 9216, 10752, 8064, 4032, 1344, 288, 36, 2, 2047 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 1:  -1+2^n

Row sums: A048473

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

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

LINKS

Table of n, a(n) for n=1..56.

FORMULA

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

3....2

7....8....2

15...24...12...2

31...64...48...16...2

First three polynomials v(n,x): 1, 3 + 2x , 7 + 8x + 2x^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] + (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[%]   (* A210203 *)

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

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

TableForm[cv]

Flatten[%]   (* A210204 *)

CROSSREFS

Cf. A210203, A208510.

Sequence in context: A226370 A054183 A188656 * A208657 A329940 A074680

Adjacent sequences:  A210201 A210202 A210203 * A210205 A210206 A210207

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 18 2012

STATUS

approved

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Last modified December 5 13:26 EST 2019. Contains 329751 sequences. (Running on oeis4.)