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A210216 Triangle of coefficients of polynomials v(n,x) jointly generated with A210215; see the Formula section. 3
1, 1, 2, 1, 3, 3, 1, 3, 7, 4, 1, 3, 8, 14, 5, 1, 3, 8, 20, 25, 6, 1, 3, 8, 21, 46, 41, 7, 1, 3, 8, 21, 54, 97, 63, 8, 1, 3, 8, 21, 55, 133, 189, 92, 9, 1, 3, 8, 21, 55, 143, 309, 344, 129, 10, 1, 3, 8, 21, 55, 144, 364, 674, 591, 175, 11, 1, 3, 8, 21, 55, 144, 376, 894 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Limiting row: even-indexed Fibonacci numbers, A001906.

n-th row sum:  -1+2*n

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

LINKS

Table of n, a(n) for n=1..74.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...2

1...3...3

1...3...7...4

1...3...8...14...5

First three polynomials v(n,x): 1, 1 + 2x , 1 + 3x + 3x^2.

MATHEMATICA

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

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

v[n_, x_] := x*u[n - 1, x] + 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[%]    (* A210215 *)

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

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

TableForm[cv]

Flatten[%]    (* A210216 *)

Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A000225 *)

Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A000225 *)

Table[u[n, x] /. x -> -1, {n, 1, z}] (* A137470 *)

Table[v[n, x] /. x -> -1, {n, 1, z}] (* A137470 *)

CROSSREFS

Cf. A210215, A208510.

Sequence in context: A291302 A278493 A180975 * A195915 A219158 A049834

Adjacent sequences:  A210213 A210214 A210215 * A210217 A210218 A210219

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 19 2012

STATUS

approved

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Last modified October 18 07:42 EDT 2019. Contains 328146 sequences. (Running on oeis4.)