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A209704 Triangle of coefficients of polynomials v(n,x) jointly generated with A209703; see the Formula section. 3
1, 3, 1, 4, 3, 2, 5, 6, 8, 3, 6, 10, 18, 14, 5, 7, 15, 33, 38, 27, 8, 8, 21, 54, 81, 83, 49, 13, 9, 28, 82, 150, 197, 170, 89, 21, 10, 36, 118, 253, 401, 448, 342, 159, 34, 11, 45, 163, 399, 736, 999, 987, 671, 282, 55, 12, 55, 218, 598, 1253, 1988, 2387, 2106 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For n>1, row n starts with n+1, followed by the n-th

triangular number, and ends in F(n+1), where F=A000045

(Fibonacci numbers).

Column 3:  A166830.

Row sums:  A048654.

Alternating row sums: 1,2,3,4,5,6,7,8,9,...

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

LINKS

Table of n, a(n) for n=1..63.

FORMULA

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

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

3...1

4...3....2

5...6....8....3

6...10...18...14...5

First three polynomials v(n,x): 1, 3 + x , 4 + 3x + 2x^2.

MATHEMATICA

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

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

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[%]  (* A209703 *)

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

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

TableForm[cv]

Flatten[%]  (* A209704 *)

CROSSREFS

Cf. A209703, A208510.

Sequence in context: A104764 A152842 A307280 * A082909 A029151 A102595

Adjacent sequences:  A209701 A209702 A209703 * A209705 A209706 A209707

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved

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Last modified October 15 21:17 EDT 2019. Contains 328038 sequences. (Running on oeis4.)