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A210213 Triangle of coefficients of polynomials u(n,x) jointly generated with A210214; see the Formula section. 3
1, 2, 1, 4, 3, 1, 7, 9, 4, 1, 12, 21, 16, 5, 1, 20, 46, 46, 25, 6, 1, 33, 94, 121, 85, 36, 7, 1, 54, 185, 289, 260, 141, 49, 8, 1, 88, 353, 653, 708, 491, 217, 64, 9, 1, 143, 659, 1409, 1800, 1499, 847, 316, 81, 10, 1, 232, 1209, 2939, 4320, 4229, 2863, 1366 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums:  even-indexed Fibonacci numbers

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

LINKS

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

FORMULA

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

v(n,x)=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

2....1

4....3....1

7....9....4....1

12...21...16...5...1

First three polynomials u(n,x): 1, 2 + x, 4 + 3x + 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_] := 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[%]    (* A210213 *)

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

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

TableForm[cv]

Flatten[%]    (* A210214 *)

CROSSREFS

Cf. A210214, A208510.

Sequence in context: A133805 A131254 A210229 * A305695 A211235 A134626

Adjacent sequences:  A210210 A210211 A210212 * A210214 A210215 A210216

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 19 2012

STATUS

approved

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Last modified October 19 21:28 EDT 2019. Contains 328244 sequences. (Running on oeis4.)