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A210742 Triangle of coefficients of polynomials v(n,x) jointly generated with A210741; see the Formula section. 3
1, 3, 2, 5, 9, 5, 7, 20, 27, 13, 9, 35, 73, 80, 34, 11, 54, 151, 252, 234, 89, 13, 77, 269, 597, 837, 677, 233, 15, 104, 435, 1199, 2225, 2702, 1941, 610, 17, 135, 657, 2158, 4956, 7943, 8533, 5523, 1597, 19, 170, 943, 3590, 9796, 19387, 27435, 26479 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with 2n-1 and ends with an odd-indexed

Fibonacci number.

Row sums: A035344

Alternate row sums: 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..53.

FORMULA

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

5...9....5

7...20...27...13

9...35...73...80...34

First three polynomials v(n,x): 1, 3 + 2x, 5 + 9x + 5x^2

MATHEMATICA

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

u[n_, x_] := 2 x*u[n - 1, x] + 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[%]     (* A210741 *)

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

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

TableForm[cv]

Flatten[%]     (* A210742 *)

CROSSREFS

Cf. A210741, A208510.

Sequence in context: A173701 A116627 A254331 * A175056 A320274 A257705

Adjacent sequences:  A210739 A210740 A210741 * A210743 A210744 A210745

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 24 2012

STATUS

approved

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Last modified September 18 20:21 EDT 2019. Contains 327181 sequences. (Running on oeis4.)