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A210797 Triangle of coefficients of polynomials u(n,x) jointly generated with A210798; see the Formula section. 3
1, 1, 1, 1, 3, 2, 1, 4, 5, 3, 1, 6, 10, 10, 5, 1, 7, 16, 22, 18, 8, 1, 9, 24, 42, 47, 33, 13, 1, 10, 33, 69, 98, 95, 59, 21, 1, 12, 44, 108, 182, 220, 188, 105, 34, 1, 13, 56, 156, 308, 444, 472, 363, 185, 55, 1, 15, 70, 220, 490, 818, 1034, 985, 690, 324, 89, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row n starts with 1 and ends with F(n), where F=A000045 (Fibonacci numbers).

Column 2: A032766

Column 3: A001859

Row sums: A099232

Alternating row sums: A008346

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

LINKS

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

FORMULA

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

v(n,x)=(x+2)*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

1...1

1...3...2

1...4...5....3

1...6...10...10...5

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

MATHEMATICA

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

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

d[x_] := h + x; e[x_] := p + x;

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

j = 0; c = 0; h = 2; p = -1; f = 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[%]    (* A210797 *)

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

TableForm[cv]

Flatten[%]    (* A210798 *)

Table[u[n, x] /. x -> 1, {n, 1, z}]   (* A099232 *)

Table[v[n, x] /. x -> 1, {n, 1, z}]   (* A006130 *)

Table[u[n, x] /. x -> -1, {n, 1, z}]  (* A008346 *)

Table[v[n, x] /. x -> -1, {n, 1, z}]  (* A039834 *)

CROSSREFS

Cf. A210798, A208510.

Sequence in context: A247641 A261876 A272336 * A222220 A271830 A193815

Adjacent sequences:  A210794 A210795 A210796 * A210798 A210799 A210800

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 26 2012

STATUS

approved

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Last modified October 17 18:58 EDT 2019. Contains 328127 sequences. (Running on oeis4.)