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A210229 Triangle of coefficients of polynomials u(n,x) jointly generated with A210230; see the Formula section. 3
1, 2, 1, 4, 3, 1, 7, 8, 4, 1, 12, 18, 13, 5, 1, 20, 38, 35, 19, 6, 1, 33, 76, 86, 59, 26, 7, 1, 54, 147, 197, 164, 91, 34, 8, 1, 88, 277, 430, 420, 281, 132, 43, 9, 1, 143, 512, 904, 1014, 792, 447, 183, 53, 10, 1, 232, 932, 1846, 2338, 2087, 1371, 673, 245, 64 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 1:  -1+F(n+1), where F=A000045 (Fibonacci numbers)

Alternating row sums: 1,1,2,2,3,3,4,4,5,5,...

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

LINKS

Table of n, a(n) for n=1..64.

FORMULA

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

v(n,x)=(x+1)*u(n-1,x)+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....8....4....1

12...18...13...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_] := (x + 1)*u[n - 1, 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[%]     (* A210229 *)

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

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

TableForm[cv]

Flatten[%]     (* A210230 *)

CROSSREFS

Cf. A210230, A208510.

Sequence in context: A131252 A133805 A131254 * A210213 A305695 A211235

Adjacent sequences:  A210226 A210227 A210228 * A210230 A210231 A210232

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 20 2012

STATUS

approved

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Last modified October 20 14:40 EDT 2019. Contains 328267 sequences. (Running on oeis4.)