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A210217 Triangle of coefficients of polynomials u(n,x) jointly generated with A210218; see the Formula section. 4
1, 2, 1, 2, 5, 1, 2, 6, 12, 1, 2, 6, 19, 27, 1, 2, 6, 20, 57, 58, 1, 2, 6, 20, 67, 160, 121, 1, 2, 6, 20, 68, 218, 424, 248, 1, 2, 6, 20, 68, 231, 680, 1073, 503, 1, 2, 6, 20, 68, 232, 775, 2028, 2619, 1014, 1, 2, 6, 20, 68, 232, 791, 2543, 5797, 6214, 2037, 1, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Limiting row:  A006012

Row sums: even-indexed Fibonacci numbers: 1,3,8,21,...

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

LINKS

Table of n, a(n) for n=1..67.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...1

2...5...1

2...6...12...1

2...6...19...27...1

First three polynomials u(n,x): 1, 2 + x, 2 + 5x + x^2.

MATHEMATICA

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

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

v[n_, x_] := x*u[n - 1, x] + 2 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[%]    (* A210217 *)

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

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

TableForm[cv]

Flatten[%]     (* A210218 *)

CROSSREFS

Cf. A210218, A208510.

Sequence in context: A132309 A144224 A122881 * A334165 A210223 A242598

Adjacent sequences:  A210214 A210215 A210216 * A210218 A210219 A210220

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 19 2012

STATUS

approved

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Last modified December 7 18:19 EST 2021. Contains 349585 sequences. (Running on oeis4.)