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A210563 Triangle of coefficients of polynomials u(n,x) jointly generated with A210564; see the Formula section. 3
1, 1, 2, 1, 3, 5, 1, 3, 10, 13, 1, 3, 11, 32, 34, 1, 3, 11, 40, 99, 89, 1, 3, 11, 41, 141, 299, 233, 1, 3, 11, 41, 152, 482, 887, 610, 1, 3, 11, 41, 153, 556, 1604, 2595, 1597, 1, 3, 11, 41, 153, 570, 1998, 5217, 7508, 4181, 1, 3, 11, 41, 153, 571, 2113, 7042 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Last terms in rows: odd-indexed Fibonacci numbers

Limiting row:  A001835

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

LINKS

Table of n, a(n) for n=1..63.

FORMULA

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

1...2

1...3...5

1...3...10...13

1...3...11...32...34

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

MATHEMATICA

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

u[n_, x_] := x*u[n - 1, x] + 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[%]  (* A210563 *)

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

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

TableForm[cv]

Flatten[%]  (* A210564 *)

CROSSREFS

Cf. A210564, A208510.

Sequence in context: A089984 A284429 A062105 * A236311 A093412 A119355

Adjacent sequences:  A210560 A210561 A210562 * A210564 A210565 A210566

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 23 2012

STATUS

approved

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Last modified October 21 03:24 EDT 2019. Contains 328291 sequences. (Running on oeis4.)