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A209758 Triangle of coefficients of polynomials v(n,x) jointly generated with A210041; see the Formula section. 3
1, 1, 3, 1, 5, 6, 1, 7, 13, 12, 1, 9, 22, 32, 24, 1, 11, 33, 63, 76, 48, 1, 13, 46, 107, 170, 176, 96, 1, 15, 61, 166, 321, 440, 400, 192, 1, 17, 78, 242, 546, 912, 1104, 896, 384, 1, 19, 97, 337, 864, 1683, 2488, 2704, 1984, 768, 1, 21, 118, 453, 1296, 2865 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums:  -1+(odd-indexed Fibonacci numbers)

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

LINKS

Table of n, a(n) for n=1..61.

FORMULA

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

v(n,x)=x*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...3

1...5...6

1...7...13...12

1...9...22...32...24

First three polynomials v(n,x): 1, 1 + 3x , 1 + 5x + 6x^2.

MATHEMATICA

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

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

v[n_, x_] := x*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[%]    (* A210041 *)

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

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

TableForm[cv]

Flatten[%]    (* A209758 *)

CROSSREFS

Cf. A210041, A208510.

Sequence in context: A181641 A049266 A089028 * A134083 A210551 A113445

Adjacent sequences:  A209755 A209756 A209757 * A209759 A209760 A209761

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 17 2012

STATUS

approved

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Last modified October 18 05:39 EDT 2019. Contains 328146 sequences. (Running on oeis4.)