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A210598 Triangle of coefficients of polynomials u(n,x) jointly generated with A210599; see the Formula section. 3
1, 2, 2, 3, 7, 5, 4, 14, 23, 13, 5, 24, 58, 72, 34, 6, 36, 119, 219, 219, 89, 7, 51, 209, 521, 777, 653, 233, 8, 68, 338, 1048, 2101, 2639, 1918, 610, 9, 88, 508, 1902, 4754, 7989, 8679, 5567, 1597, 10, 110, 730, 3180, 9565, 20055, 29062, 27844, 16003 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with n and ends with an odd-indexed

Fibonacci number. For a discussion and guide to related

arrays, see A208510.

LINKS

Table of n, a(n) for n=1..54.

FORMULA

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

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

2...2

3...7....5

4...14...23...13

5...24...58...72...34

First three polynomials u(n,x): 1, 2+ 2x, 3 + 7x + 5x^2.

MATHEMATICA

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

u[n_, x_] := x*u[n - 1, x] + (x + 1)*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[%]    (* A210598 *)

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

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

TableForm[cv]

Flatten[%]    (* A210599 *)

CROSSREFS

Cf. A210599, A208510.

Sequence in context: A208762 A209746 A267822 * A051301 A002583 A068519

Adjacent sequences:  A210595 A210596 A210597 * A210599 A210600 A210601

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 24 2012

STATUS

approved

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Last modified October 14 00:05 EDT 2019. Contains 327988 sequences. (Running on oeis4.)