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A210038 Triangle of coefficients of polynomials v(n,x) jointly generated with A210037; see the Formula section. 3
1, 3, 1, 7, 4, 1, 15, 12, 5, 1, 31, 32, 18, 6, 1, 63, 80, 56, 25, 7, 1, 127, 192, 160, 88, 33, 8, 1, 255, 448, 432, 280, 129, 42, 9, 1, 511, 1024, 1120, 832, 450, 180, 52, 10, 1, 1023, 2304, 2816, 2352, 1452, 681, 242, 63, 11, 1, 2047, 5120, 6912, 6400 (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..59.

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....1

7....4....1

15...12...5....1

31...32...18...6...1

First three polynomials v(n,x): 1, 3 + x , 7 + 4x + x^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] + (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[%]    (* A210037 *)

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

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

TableForm[cv]

Flatten[%]    (* A210038 *)

CROSSREFS

Cf. A210037, A208510.

Sequence in context: A104709 A110814 A275599 * A319076 A286513 A193970

Adjacent sequences:  A210035 A210036 A210037 * A210039 A210040 A210041

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 17 2012

STATUS

approved

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Last modified October 17 16:37 EDT 2019. Contains 328119 sequences. (Running on oeis4.)