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A210035 Triangle of coefficients of polynomials u(n,x) jointly generated with A210036; see the Formula section. 3
1, 3, 6, 2, 11, 6, 4, 19, 16, 12, 8, 32, 36, 36, 24, 16, 53, 76, 88, 80, 48, 32, 87, 152, 204, 208, 176, 96, 64, 142, 294, 444, 520, 480, 384, 192, 128, 231, 554, 932, 1208, 1280, 1088, 832, 384, 256, 375, 1024, 1896, 2704, 3136, 3072, 2432, 1792, 768 (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..55.

FORMULA

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

v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,

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

EXAMPLE

First five rows:

1

3

6....2

11...6....4

19...16...12...8

First three polynomials u(n,x): 1, 3, 6 + 2x.

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. A210036, A208510.

Sequence in context: A210187 A210189 A257506 * A210199 A268717 A002516

Adjacent sequences:  A210032 A210033 A210034 * A210036 A210037 A210038

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 16 2012

STATUS

approved

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Last modified November 30 08:19 EST 2021. Contains 349419 sequences. (Running on oeis4.)