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A210806 Triangle of coefficients of polynomials v(n,x) jointly generated with A210805; see the Formula section. 4
1, 0, 2, 1, 1, 3, 0, 3, 3, 5, 1, 2, 8, 7, 8, 0, 4, 8, 19, 15, 13, 1, 3, 15, 25, 42, 30, 21, 0, 5, 15, 46, 67, 89, 58, 34, 1, 4, 24, 58, 128, 164, 182, 109, 55, 0, 6, 24, 90, 186, 330, 378, 363, 201, 89, 1, 5, 35, 110, 300, 536, 804, 833, 709, 365, 144, 0, 7, 35, 155 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Row n ends with F(n), where F=A000045 (Fibonacci numbers).
Column 1: 1,0,1,0,1,0,1,0,...
Alternating row sums: signed Fibonacci numbers.
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=(x+2)*u(n-1,x)+(x-1)*v(n-1,x)-1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
0...2
1...1...3
0...3...3...5
1...2...8...7...8
First three polynomials v(n,x): 1, 2x, 1 + x + 3x^2
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
d[x_] := h + x; e[x_] := p + x;
v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
j = 0; c = 0; h = 2; p = -1; f = -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[%] (* A210805 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210806 *)
CROSSREFS
Sequence in context: A155993 A353630 A341091 * A147867 A227431 A114118
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 27 2012
STATUS
approved

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Last modified February 23 17:37 EST 2024. Contains 370283 sequences. (Running on oeis4.)