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A209774 Triangle of coefficients of polynomials v(n,x) jointly generated with A209773; see the Formula section. 3
1, 2, 3, 2, 7, 8, 3, 12, 25, 21, 3, 19, 56, 84, 55, 4, 26, 103, 227, 269, 144, 4, 36, 169, 486, 848, 833, 377, 5, 45, 259, 914, 2078, 2999, 2518, 987, 5, 58, 372, 1565, 4393, 8277, 10192, 7475, 2584, 6, 69, 518, 2503, 8342, 19420, 31269, 33600, 21881 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Last term in row n: F(2n), where F=A000045, the Fibonacci numbers

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...3

2...7....8

3...12...25...21

3...19...56...84...55

First three polynomials v(n,x): 1, 2 + 3x , 2 + 7x + 8x^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];

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[%]    (* A209773 *)

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

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

TableForm[cv]

Flatten[%]    (* A209774 *)

CROSSREFS

Cf. A209673, A208510.

Sequence in context: A210564 A208930 A122076 * A271322 A170842 A014784

Adjacent sequences:  A209771 A209772 A209773 * A209775 A209776 A209777

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 15 2012

STATUS

approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)