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A209574 Triangle of coefficients of polynomials v(n,x) jointly generated with A209573; see the Formula section. 3
1, 2, 3, 3, 7, 5, 4, 14, 20, 7, 5, 24, 52, 45, 9, 6, 37, 110, 155, 86, 11, 7, 53, 203, 403, 389, 147, 13, 8, 72, 340, 882, 1240, 856, 232, 15, 9, 94, 530, 1712, 3204, 3322, 1702, 345, 17, 10, 119, 782, 3040, 7170, 10088, 7962, 3125, 490, 19, 11, 147, 1105 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Combinatorial limit of row n satisfies linear recurrence

r(n)=4*r(n-1)-r(n-2) with r(1)=1 and r(2)=3.  For a

discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..58.

FORMULA

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

v(n,x)=2x*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...3

3...7....5

4...14...20...7

5...24...52...45...9

First three polynomials v(n,x): 1, 2 + 3x , 3 + 7x + 5x^2.

MATHEMATICA

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

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

v[n_, x_] := 2 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[%]   (* A209573 *)

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

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

TableForm[cv]

Flatten[%]   (* A209574 *)

CROSSREFS

Cf. A209573, A208510.

Sequence in context: A088100 A097359 A208525 * A079387 A141061 A256447

Adjacent sequences:  A209571 A209572 A209573 * A209575 A209576 A209577

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 11 2012

STATUS

approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)