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A210034 Triangle of coefficients of polynomials v(n,x) jointly generated with A210033; see the Formula section. 3
1, 2, 1, 4, 2, 1, 7, 5, 2, 1, 12, 10, 6, 2, 1, 20, 20, 13, 7, 2, 1, 33, 38, 29, 16, 8, 2, 1, 54, 71, 60, 39, 19, 9, 2, 1, 88, 130, 122, 86, 50, 22, 10, 2, 1, 143, 235, 241, 187, 116, 62, 25, 11, 2, 1, 232, 420, 468, 392, 267, 150, 75, 28, 12, 2, 1, 376, 744, 894, 806 (list; table; 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..70.

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

2....1

4....2....1

7....5....2...1

12...10...6...2...1

MATHEMATICA

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

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. A210033, A208510.

Sequence in context: A209439 A133938 A239829 * A074586 A277812 A134586

Adjacent sequences:  A210031 A210032 A210033 * A210035 A210036 A210037

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 16 2012

STATUS

approved

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Last modified October 20 16:12 EDT 2019. Contains 328268 sequences. (Running on oeis4.)