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A210740 Triangle of coefficients of polynomials v(n,x) jointly generated with A210739; see the Formula section. 3
1, 2, 2, 2, 6, 5, 2, 7, 18, 13, 2, 7, 25, 53, 34, 2, 7, 26, 86, 154, 89, 2, 7, 26, 96, 286, 443, 233, 2, 7, 26, 97, 348, 926, 1264, 610, 2, 7, 26, 97, 361, 1234, 2935, 3582, 1597, 2, 7, 26, 97, 362, 1334, 4280, 9143, 10092, 4181, 2, 7, 26, 97, 362, 1350, 4875 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n ends with odd-indexed Fibonacci numbers.

Limiting row: A001075.

Row sums: A003462.

Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...

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

LINKS

Table of n, a(n) for n=1..62.

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

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

EXAMPLE

First five rows:

1

2...2

2...6...5

2...7...18...13

2...7...25...53...34

First three polynomials v(n,x): 1, 2 + 2x, 2 + 6x + 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*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[%]   (* A210739 *)

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

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

TableForm[cv]

Flatten[%]   (* A210740 *)

CROSSREFS

Cf. A210739, A208510.

Sequence in context: A211391 A309078 A241543 * A209820 A145890 A097091

Adjacent sequences:  A210737 A210738 A210739 * A210741 A210742 A210743

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 24 2012

STATUS

approved

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Last modified November 24 10:26 EST 2020. Contains 338612 sequences. (Running on oeis4.)