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A210741 Triangle of coefficients of polynomials u(n,x) jointly generated with A210742; see the Formula section. 3
1, 1, 3, 1, 5, 8, 1, 7, 19, 21, 1, 9, 34, 65, 55, 1, 11, 53, 141, 210, 144, 1, 13, 76, 257, 534, 654, 377, 1, 15, 103, 421, 1111, 1905, 1985, 987, 1, 17, 134, 641, 2041, 4447, 6512, 5911, 2584, 1, 19, 169, 925, 3440, 9038, 16837, 21557, 17345, 6765, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Rows end with even-indexed Fibonacci numbers

Row sums: A007070

Alternating row sums:  signed powers of 2

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

LINKS

Table of n, a(n) for n=1..56.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...3

1...5...8

1...7...19...21

1...9...34...65...55

First three polynomials u(n,x): 1, 1+ 3x, 1 + 5x + 8x^2.

MATHEMATICA

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

u[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;

v[n_, x_] := (x + 1)*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[%]     (* A210741 *)

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

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

TableForm[cv]

Flatten[%]     (* A210742 *)

CROSSREFS

Cf. A210742, A208510.

Sequence in context: A302191 A261712 A038738 * A208760 A116647 A063858

Adjacent sequences:  A210738 A210739 A210740 * A210742 A210743 A210744

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 24 2012

STATUS

approved

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Last modified October 17 15:32 EDT 2019. Contains 328116 sequences. (Running on oeis4.)