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A210749 Triangle of coefficients of polynomials u(n,x) jointly generated with A210750; see the Formula section. 3
1, 3, 1, 6, 7, 1, 11, 21, 15, 1, 19, 53, 60, 31, 1, 32, 118, 191, 155, 63, 1, 53, 246, 514, 593, 378, 127, 1, 87, 489, 1261, 1863, 1683, 889, 255, 1, 142, 941, 2890, 5233, 6029, 4501, 2040, 511, 1, 231, 1767, 6311, 13527, 19026, 18068, 11543, 4599 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with -2+F(n+3) and ends with 1, where F=A000045 (Fibonacci numbers).

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..53.

FORMULA

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

v(n,x)=(x+1)*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....1

6....7....1

11...21...15...1

19...53...60...31...1

First three polynomials u(n,x): 1, 3+ x, 6 + 7x + x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*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[%]    (* A210749 *)

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

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

TableForm[cv]

Flatten[%]    (* A210750 *)

CROSSREFS

Cf. A210750, A208510.

Sequence in context: A208766 A259454 A209696 * A199662 A280293 A226483

Adjacent sequences:  A210746 A210747 A210748 * A210750 A210751 A210752

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 25 2012

STATUS

approved

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Last modified October 19 16:08 EDT 2019. Contains 328223 sequences. (Running on oeis4.)