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A210798 Triangle of coefficients of polynomials v(n,x) jointly generated with A210797; see the Formula section. 3
1, 2, 2, 1, 3, 3, 2, 5, 7, 5, 1, 6, 12, 13, 8, 2, 8, 20, 29, 25, 13, 1, 9, 27, 51, 62, 46, 21, 2, 11, 39, 84, 125, 129, 84, 34, 1, 12, 48, 126, 224, 284, 258, 151, 55, 2, 14, 64, 182, 374, 562, 622, 505, 269, 89, 1, 15, 75, 250, 580, 1008, 1328, 1315, 969, 475 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with A109613(n) and ends with F(n+1), where F=A000045 (Fibonacci numbers).

Column 2: A114113

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

LINKS

Table of n, a(n) for n=1..65.

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

2...2

1...3...3

2...5...7....5

1...6...12...13...8

First three polynomials v(n,x): 1, 2 + 2x, 1 + 3x + 3x^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. A210797, A208510.

Sequence in context: A011373 A321783 A177352 * A117501 A117915 A294453

Adjacent sequences:  A210795 A210796 A210797 * A210799 A210800 A210801

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 26 2012

STATUS

approved

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Last modified October 14 07:31 EDT 2019. Contains 327995 sequences. (Running on oeis4.)