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A210033 Triangle of coefficients of polynomials u(n,x) jointly generated with A210034; see the Formula section. 3
1, 3, 6, 1, 11, 3, 1, 19, 8, 3, 1, 32, 18, 9, 3, 1, 53, 38, 22, 10, 3, 1, 87, 76, 51, 26, 11, 3, 1, 142, 147, 111, 65, 30, 12, 3, 1, 231, 277, 233, 151, 80, 34, 13, 3, 1, 375, 512, 474, 338, 196, 96, 38, 14, 3, 1, 608, 932, 942, 730, 463, 246, 113, 42, 15, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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)+v(n-1,x)+1,

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

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First five rows:

1

3

6....1

11...3...1

19...8...3...1

First three polynomials u(n,x): 1, 3, 6 + x.

MATHEMATICA

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

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

v[n_, x_] := u[n - 1, x] + 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[%]    (* A210033 *)

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

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

TableForm[cv]

Flatten[%]    (* A210034 *)

CROSSREFS

Cf. A210034, A208510.

Sequence in context: A152202 A210039 A026250 * A209144 A130724 A120229

Adjacent sequences:  A210030 A210031 A210032 * A210034 A210035 A210036

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Mar 16 2012

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)