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A210203 Triangle of coefficients of polynomials u(n,x) jointly generated with A210204; see the Formula section. 3
1, 3, 7, 2, 15, 10, 2, 31, 34, 14, 2, 63, 98, 62, 18, 2, 127, 258, 222, 98, 22, 2, 255, 642, 702, 418, 142, 26, 2, 511, 1538, 2046, 1538, 702, 194, 30, 2, 1023, 3586, 5630, 5122, 2942, 1090, 254, 34, 2, 2047, 8194, 14846, 15874, 11006, 5122, 1598, 322 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 1: -1+2^n

Row sums: 3^(n-1)

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..54.

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

7....2

15...10...2

31...34...14...2

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

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. A210204, A208510.

Sequence in context: A246377 A260421 A237427 * A318467 A245611 A063041

Adjacent sequences:  A210200 A210201 A210202 * A210204 A210205 A210206

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Mar 18 2012

STATUS

approved

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Last modified October 19 09:21 EDT 2018. Contains 316339 sequences. (Running on oeis4.)