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A210036 Triangle of coefficients of polynomials v(n,x) jointly generated with A210035; see the Formula section. 3
1, 2, 2, 4, 4, 4, 7, 10, 8, 8, 12, 20, 24, 16, 16, 20, 40, 52, 56, 32, 32, 33, 76, 116, 128, 128, 64, 64, 54, 142, 240, 312, 304, 288, 128, 128, 88, 260, 488, 688, 800, 704, 640, 256, 256, 143, 470, 964, 1496, 1856, 1984, 1600, 1408, 512, 512, 232, 840 (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..57.

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....2

4....4....4

7....10...8....8

12...20...24...16...16

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

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] + 2 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[%]    (* A210035 *)

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

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

TableForm[cv]

Flatten[%]    (* A210036 *)

CROSSREFS

Cf. A210035, A208510.

Sequence in context: A120456 A115383 A219156 * A304230 A305586 A305040

Adjacent sequences:  A210033 A210034 A210035 * A210037 A210038 A210039

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 16 2012

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)